There's something I can't really get a hold on in these games and that is: why doesn't everyone learn magic?

Apparently, in terms of gameplay, any character can raise magical skills to some pretty practical levels, yet many NPC don't use it. I do understand signs, to a lesser extent, race, play a big role just how good a mage one can become but even so, a nord warrior can still benefit from healing spells and whatnot even if they're not very potent.

Now I think there's a discrepancy here: magic certainly doesn't appear to be very widespread as far as I can tell from books and general lore. There was one book about some guy who learned, with some difficulty, a waterbreathing spell to dive down to something where he died because the spell ran out, but I haven't found any other example of "commoners" learning magical skills. Not that I've read many, which is why I'm asking here:

Is magic supposed to be accessed by everyone? Or just to those with certain traits? How does the Elder Scrolls universe compare to... say the Baldur's Gate or Dragon Age universe (where only a select few could use magic)?

Magic is portrayed very badly in the games from the player's perspective IMO, more so with Oblivion than the rest. Te idea that everybody is born with a fireball and healing spell is quite wrong, and was most likely put for the player so that they could experience part of the magic system before deciding what class they wanted to be, that was sort of the intention of the tutorial, to give you a taste of all the different styles of playing in the beginning.

You are right though, magic isn't meant to be easily learnt and used, why do you think that one of the challenges to get training from the master magic trainers were simple things like summoning a faded wraith, or staying underwater for 30 minutes or something. These things are meant to be very difficult to do, but the game mechanics portray that poorly.

When you're a peasant scrounging a living out of the ground, you don't have time to learn magick and simultaneously sustain yourself, regardless of how helpful it may be even to the task at hand. As for those who aren't subsistence farmers, it's doubtful many can afford the training it takes to learn magick, and with the alternative being going out and killing monsters to train your skill DIY-style most folks probably don't have the stomach for it.

That said, if you check the TESCS most individuals do actually have some small magickal potential and a handful of spells available to them, they just never seem to use them (likely for gameplay reasons).

Magic is creatia. Every created thing is magic. It's quite pervasive, as you can imagine.

However, use of magic is supposed to be esoteric. This is an example of the Tamriel you read of versus the one you play in.

A few characters use simple healing spells with no problem, esp elves. So it sort of fits in with elves being more magical. Plus our character put in a lot of practice to reach the levels that we did and not a lot of people have the opportunity to do that (like people have said on this thread). Plus if you have no spells to train with that puts a downer on your ambitions. Not everyone would pay the wages of a year to learn a simple spell that doesn't do much, so they can train in that school. That's what the Mages Guild is/was for. If you need magic services you pay them a modest sum to do stuff for you. And if you have more time/inclination/money you can join the mages guild and start training with them. Which is what the player does i guess.

Unless you have an inner talent which manifests at childhood. Read the Mages Guild charter Manual of Spellcraft for a brief introduction

That's why I'm glad they're gone-ish. They demystified mysticism.

I wonder how the Synod and The College of Whispers will deal with magic. Or even if there is some rivalry between them of some sorts.

Apparently the Synod teaches spells for a membership fee, so they sound similar enough to the Mages' Guild in that specific regard. Perhaps Bethesda's real reason for doing away with the Mages' Guild is the name is boring (and therefore wrong).

Until recently, the Mage's Guild had an exclusive monopoly on magic in most parts of the empires, in that the only legal way to learn magic is to go through the mages guild. There was a quest in Morrowind about this in the telvanni questline where you had to go to the redoran council house and convince the redoran councillors to oppose the mage's guild monopoly.

I remember another quest in Morrowind for the mage's guild, where an argonian mage was teaching magic without a license. Of course, you had to shake him up. Obviously, the only way to become a mage is through the mages guild, and I assume they charge well.