More and more people are capable of using magic in later games. In Skyrim, every viable character includes restoration (in fact everyone starts with a fire spell regardless of race). But go all the way back and you find games where non-mages can cast a single spell and it has 5% chance to work.
I find Skyrim trivialises magic to the point where it breaks immersion. Any noob can cast a healing spell. It may not be a very good one, but that doesn't matter outside combat - not a concern in the game, but this is now officially a world where everyone can heal themselves in a few hours from the brink of death.
Likewise, untrained individuals can summon spirit wolves and shoot lightning bolts.
If you're concerned about racial bonuses, take a look at Resplendent Racials. Altmer in RR are obviously a more "magical" race, but this manifests as a low health and high stamina/magicka playstyle because they can tap their stats to heal themselves. Orcs are more "physical", but they get rewarded for not taking much damage, which in turn benefits mages. The end result is that every race is reasonably adept at every build even if it doesn't look like it. This is on purpose.