I agree. "Summoning" animals with normal Hermetic CrAn (or other things with CrFo) seems to easily get you a "summoner" character. Either make them formulaic spells with Duration (which means that whatever you summon will be resisted as magical creations) or make them momentary rituals (which means the beasts won't be resisted, but takes ages to cast, and requires vis to burn).
You might also need a ReAn (or InAn) effect to order your menagerie about once you've summoned it.
Yeah I've got to admit I was overlooking the mundane animals option. CrAn is certainly an option the magnitudes aren't too out of hand even with durations and range. You do have to worry about penetration and control. But it's not undooable.
Divination and timetravel strike me as the two big things that vanilla Hermetic magic can't do, but which literary and "historic" magi tend to do.
Sometimes, when I'm a player I wish it could do these, but when I'm a storyguide, I'm generally happy it can't. Which probably explains why wizard-sorts in most RPGs can't do these very effectivelly either.
Diviniation you can do horoscopes and/or have visions. It's effectively limited to what the SG wants you to know, but it's there.
Timetravel... well, players prepared to abuse a regio can do it. Find one where time passes quicker inside than out, and you can spend extra seasons in a year. Find one in which time passes slower and you can hole up in it waiting for time to pass outside.
Travelling backwards in time is impossible for hermetic magi as far as we know, but that's no guarantee 
That isn't Hermetic magic.
It's certainly possible to have timetravel in ArM. As you say, the storyguide just provides a mechanism like a regio. There's no reason why you can't have a regio where time goes backwards too. No problem.
However, that's also not Hermetic magic. It would only be Hermetic magic if there were spell guidelines on how to deliberately create regios with specifically these properties; which there don't seem to be.
If a person's horoscope is usable as a sympathetic or even arcane connection, which the rules imply it is, it's covered within magic theory. That makes it usable as hermetic magic. Admittedly, that sort of prophecy is entirely with it's own flaws, such as how the heck you interpret it...
The current example, of course, being Harry Potter. The prophecy in that has at least 8 different interpretations possible from the first read through without any other details. And a horoscope is even less clear and accurate than that.
It's Artes Liberales actually to cast a horoscope. But that isn't using the horoscope for prophecy (i.e. Divination) though. It is using it as a boost to Penetration (or potentially a way to target spells if you have a way to use a horoscope as an Arcane Connection).
It would certainly make sense to use a horoscope for Divination, afterall that is what they are supposedly for in real life, however there aren't any Hermetic spells (or other vanilla Hermetic mechansims) that actually use horoscopes for Divination. At best you can use a horoscope with Hermetic spells to help scrying, which is close, but isn't Divination.
There are many "stock" fantasy (or fantasy RPG) concepts that are not, as a rule, part of the AM canon - different planes (for travel or natives to those planes), time travel, resurrection/reincarnation (on a relatively immediate basis, as opposed to a more natural element of birth), magical "force" effects, the immediacy of religious interaction (casually and reliably calling upon "your deity" for direct aid), psionics (that are specifically separate from "magic"), some elements/models of "the unliving", etc.
However, many could easily be introduced via extreme non-hermetic magical types, and seeing how Hermetic magi address them could be interesting.
Yeah player controlled Time Travel is nearly impossible to run. There are games that have limited PC driven time travel (GURPS, BTRC's TimeLords, The Time Lord RPG, Transdimensional TMNT, Most all Super hero Games. many more not on my shelf) but present in games or not there are often "Time" spells like Time Stop, Haste, Slow and various Do-over type spells. That Other Mage game had full on time magic while basically saying actual time travel is off the table. (Lest caveat creatures come and erase your existance)
The four realms and regios don't seem to be functionally much different to alternative planes?
Although certainly not easy for Hermetic magic, there are specific guidelines for Hermetic resurrection. Also resurrection is a big deal in Mythic Europe; it features heavily in the main religion.
What about standard Hermetic ReTe effects like Unseen Arm, and Unseen Porter and equivalents.
Hermetic magic doesn't have anything to do with this (unless perhaps in-character one sees The Gift itself as an function of some sort of deity's power; like Hermes/Thoth/Mercury).
However, in Mythic Europe more broadly there certainly is immediate, effective, religious interaction. The sacraments all do something directly. Miracles happen. Relics have supernatural properties that can be reliably activated. And any number of pagan "deities" are directly active, as pagan deities are just powerful (or even weak) magical or faerie or infernal creatures. For example, anybody sufficiently advanced along a Forest Path receives direct aid from the forest spirit.
It is difficult to see what capabilities of "psionics" are actually missing from Hermetic magic.
Aside from (loosely speaking) the Planes of Good, Evil, and "Dreams"( Faerie?), nope. And even those are hardly identical to an actual "different plane of existence".
(Non-)Parallel planes of existence similar to ours? Nope.
And forgive me if I don't include a laundry-list of the more exotic and creative ones.
Those are trivial TK effects. Even Wards specific to Hermetic Forms are far more limited than "Force". Many systems simply have "magical barriers" that work against anything and everything - there is no "why" or "what", they just work. Like "magic missiles" - the magic itself is creating the force, without any specific relationship to or concern for "Form".
Perhaps(?) some Rego effects with all 10 Forms could come close, but the resulting effect would be so high-level that it would be prohibitive. Plus it would require a Ritual, adding to the distance between that and Hermetic effects.
None of what you say addresses what I said. "Casually and reliably" - as in the equivalent of any Hermetic mage's magic effect (which is what we're talking about). Zip-swoosh, my god does magic for anyone I choose, no doubt about it, next show on the hour. Is he dead? Not any more! That wound? gone for good.
All day, every day. Some minor and limited elements similar to that may exist in the ME world, but not in the Hermetic model.
Always sorry to hear of such vision problems. Try re-reading the short section that you quoted from me and pay attention to the "specifically separate from "magic" part. A Hermetic mage may be able to duplicate most of an effect, but not the part where "it's not magic" - which is the model for many such examples in the broader canon of "fantasy". 
But what does that actually mean in play? How would a story where the player characters went to "a different plane" be any different from a story where the characters went to a regio or went to the faerie/magic/divine/infernal realm?
I'm not sure what the problem in-play would be. If I wanted a "Force Magus" who moved stuff around and errected mystical barriers, then I'd just create a Rego specialist. Sure he might sometimes need to pick from a suite of 10 spells (one for each Form) to do what a character in some other game might be able to do with one "spell". But that just seems to be an issue around the amount of ink used on the character sheet. It doesn't seem to mean anything in play.
Isn't that exactly how relics work?
Sure, Hermetic magi are not clerics. But in your post you listed things that were supposedly "not part of the AM canon".
Does that make any difference? Say, I want to make a character that looks like a psionist from some other game. If I can make a Hermetic magus that can do similar things, what's the problem in-play?
Also, do Supernatural Abilities count as "not magic". Second Sight, Dowsing, Animal Ken, Enchantment, etc...
Well for my purposes, it's a matter of casualness and player control. In many settings of that Other Game there is an expectation that High Powered spellcaster's can and do freely travel to other dimensions. In ArM there isn't really any go to Heaven spells, or even go to Arcadia or the Magic Realm. So while a player might desire a character who can storm the gates of Hell. It should be clear that those gates are unlikely to be one planer travel spell away. It's not a weakness of either system just a difference. One that can come up if a player tries to make "any" kind of wizard they can think of.
For someone with a good understanding of the conceits of the ArM world and the limitations of Hermetic magic it matters very little. If you create a force mage you know that you have to "fake it to make" it in many cases. The player who keeps trying to make glowey constructs of "pure force" is going to be frustrated.