Hmm. Good question!
To some extent "I don't know" - because I don't know how everyone else runs stuff 
But to try to answer....
I love the potentials of Ars Magica - both the potential for breadth and the potential for depth. So, on the one hand I want medieval society to remain "intact" - for the existence of the Order and other powers to not make a nonsense of the mundane world - because I want to examine the depth of the world. On the other hand I love the potential to tell weirder stories - Hermetic magic, ghost stories, etc. - and I want to leave the potential to tell a breadth of stories. The question is how to juggle both of those.
So you can see different approaches in different covenants:
- Some are very subtly woven into mundane society - Burnham and Schola Pythagoranis, for example.
- Some are pushed out to the fringes or are hidden so that they don't impact mundane society (Sanguis Vento, Rossan).
- Some essentially exist outside mortal society (Murkfell and Tintagel).
I also really like thinking through the implications of different parts of a coherent world. For example, if established covenants are picky about who they let in - there is no safety net - what happens to the magi who fail to secure either membership of a covenant or funding for a new venture? That's where Rossan came from. Many of the covenants came from thinking through these kinds of what-ifs.
A storgyuide could run anything from rambling, high-fantasy quests through the Regiones of Murkfell, to kitchen-sink-drama soap-opera plots around Schola Pythagoranis, but I want players to be able to explore a range within one setting - delving into high-magic, high-combat "dungeons" under Blackthorn one day, then scheming with thieves in the chambers outside Rossan before sailing south to enjoy the faerie weirdness of Tintagel, then going home and having a dream of Immanola's Hall which gives them a nudge to go investigate a completely mundane murder mystery... with all those elements still working within the same world, without them colliding with each other.
To make that work I will balance a few different things - some drawn from Ars cannon, and some not. So, for a canon example, when Regiones were first introduced (3rd ed?) I was sceptical, but I'm now a huge fan, as they allow different parts of the world to remain clearly separated. On the other hand, I will bolster parts of medieval belief to maintain balance within the mundane world (you remarked on that with the Divine protection idea), and I really enjoy the tensions that emerge when we take medieval ideas seriously (e.g. I play it that mainstream Catholic late-12th century doctrine is, metaphysically, correct; this gets really fun when modern players find they are searching for some nice relatable modern-minded humanists, or sympathising with the Cathars (who, let's be honest, made some good points!) but finding actually that the Catholic liturgy and institutions are the things most reliably standing between them and eternal damnation / the forces of hell). One big point is that I keep to the idea of the supernatural being inherently unreliable and suspicious - I go much more Art of magic than Science of magic, so anything that looks like a reliable magical machine is probably just a plot hook for something really bad happening (e.g. I do have Mercere portals in the game, because I try not to cut out too much canon stuff, but the NPCs tend to remind PCs that to use them you'd have to be truly desperate). I also have a couple of house rules to bring the rules back into line with the apparent assumptions of the game - e.g. I think it is easy to underestimate just how profoundly the published Tractatus rules will impact the Order, so I have reworked tractatus to make them rarer and more marvellous. Over all, though, I try to do this with broad thematic house-rules, rather than additional tweaks to an already complex rules system.
So to come back to your question....
I want there to be space for high fantasy epicness, but away from the mundane world. The game is rooted in the mundane, and the fantastical then becomes more remarkable for it.
So the saga I'm running at the moment, typically, players get about 5 pawns of vis a year per mage, and spend most of their time dealing with relatively mundane issues (a murder-mystery, a kidnapping, their friendly merchant being pushed to the brink of bankruptcy by a dishonest warlord), but the mundane issues build up to occasional big epic finales (they just dealt with a rogue apprentice who was trying to set himself up as the lord of a forest, I'm hoping they will take the bait and get involved with Blackthorn's researches so they can be in the midst of the carnage when it all goes wrong, and they find themselves standing between an ancient ghost and a powerful (magic?) spirit who both have opposing views of how the mundane world should be "better ruled"). Probably one third covenant/mage-stuff, one third mundane plots, one third leading up to the magical finales.
That was an essay - but hopefully it sort of answers the question?
