Integration is as easy or as difficult as the troupe wants to make it - in all scenarios in which I've been in, the opportunity has pretty much fallen into the PC's laps. (Runic artifacts, Hedge NPC's, spirits with non-hermetic powers, etc.) Actively going out and seeking a specific integration? yes. That requires focused research and years of planning...or it just requires that you find one of your grogs that happens to have an interesting supernatural virtue (such as Shapeshifting). Or it requires that you design your character with the requisite hooks. Personally, when I've designed a lab-rat style magi, I've had all the integration Hooks built into the Virtue/Flaw/history of the character. Your playstyle may be different.
Also note that some sources of Integration are ridiculously easy to find - such as, in my experience, Second Sight - it seems that every PC has at least one grog that has that one. So much so that, in-game, it makes me wonder why the Bonisagus haven't bothered to pick up the magical gold that is right outside their doorstep - or in some cases, literally inside their labs. From a metagame perspective, this is understandable: it's because the books give lots of options if players want to look into that sort of thing. In-game, though, the best response I've heard of is a combination of:
- The order is just now fully recovering from the Schism war, and hasn't been able to devote as much time to research as it has in the past.
- The order HAS been doing integration research - that's what the State of the Art of 1220 looks like.
- Bonisagus don't necessarily want to study what's easy, but rather what's interesting to them. (as suggested in HoH:TL)
- Hermetics tend to be snobby, and can't see the power and utility of (for example) Folk Witch magic - even though Folk Witches are apparently a relatively common tradition.
There's no indication that they aren't. I usually use point #2 in this case: Ars 5th edition is the result of the most recent Hermetic research up to date. All of the Hermetic virtues are (potentially) examples of partially-integrated magic systems; Elemental Magic (from the Elementalists), or Flexible Formulaic Magic (from...the Grugach?) are two possible sources.
HoH:TL, pg. 26-27 give the rough likelihood of any given type of Breakthrough to be made: Minor breakthroughs really ARE supposed to be common, if you could get Magi to study them. A Fast-paced saga could reasonably have a PC create a Major breakthrough during their timeline, while Hermetic breakthroughs are incredibly rare. Which suggests that a dedicated research player should be able to accrue 90 Breakthrough points in...well, I guess a century or so.
As such, if you're going to be doing percentages, assuming half of the Bonisagus are doing research: yes. There should be a major breakthrough at least every decade. In fact, HoH:TL gives you four examples of them (parma folds, Figurine magic, aspected magic, etc.), as well as the means by which they are published (the Folios.)
In looking through Magi of Hermes, at least 2 of them create Breakthroughs in their lifetime - getting rid of the Sterility due to the Longevity rituals, and Hermetic Metamorphosis. Others include new Guidelines, although I'm not sure if those are just clarifications, or actual creations by them. And in looking at the timelines, the time required looked to be (roughly) correct: the minor Breakthrough took ~25 years or so, while the Major Breakthrough is almost halfway there at 45 years. (Note that neither of these characters have Luck.)
The only evidence that we have of (Hermetic) discoveries not being common is the comment in the HoH:TL, where it comments that the Last Hermetic discovery was Parma, and that was done a couple of hundred years ago. Another likely possibility include the idea that only the PC's are PC's - and as such only they have access to the GM who tells them what is possible and what isn't - as it's entirely possible for OR to simply be Impossible, but to not know this until decades into it. As such, there could very well be numerous Bonisagus out there doing experiments that ultimately result in nothing more than quirky spells.
And, if we go on the idea that Hermetic Breaktrhoughs are difficult, just from a time perspective that's the case - if it takes ~100 years to develop a major breakthrough, it would take ~120 to 130 years for a Hermetic one. And that starts to get into "only the most heavily-optimized characters can do this, and only if they've been obsessing about it their entire lives."
Regarding why more magi don't collaborate: well, the OR rules themselves explicitly state why - there are personality conflicts and arguments on who gets the credit. In other words: short-sighted human nature. It looks like magi consider themselves "Proud arteurs making a magnum opus" rather than "researchers coming together to expand the common pool of knowledge."
So...there y'go. Yes. Breakthroughs should be much more common than they are in most people's games. However, as Ars doesn't have an official timeline, there's no real resource for (example) published Breakthroughs via the Folios as part of the background fluff. Personally, I've thought of doing so, simply as an interesting exercise in worldbuilding. However, I have not yet done so.