Paladin started as a Fighter subclass in 1E, while Fighter-Mage was originally a multiclass.
I could see undoing this before eliminating the mage subclass. Instead of moving Fighter-Mage out, move Paladin, Ranger and Barbarian back into fighter. I could also see Warlock and Sorcerer as subclasses of Wizard, along with things like Bladesinger, but I like having Eldritch Knight where it is.
See I totaly disagree with this and based on what you see at the table, most playing fighters do not see their characters as non-magic.
I get that there is a portion that do, mostly on message boards, but every single fighter I have seen played in 5E past about level 5 has had some kind of magic, every single one. A substantial number, easily 20% have had spells. I don't think the non-magic fighter is viable for modern players.
Players want magic, that is why the game is getting more magic focused. Spells are a key component, but not the only one.
Considering magic is a choice, I think it is clear the reason is players want magic.
From my POV one option is all you need to make it available, but when people refuse to play even that option without magic your argument starts to fall flat.
Even when playing with a relatively rare Champion or Battlemaster fighter with no racial magic; that player is usually actively looking for a magic weapon, or sometimes even whining to the DM about not having one if she gets to level 4 or sowithout one.
No one at the modern table is actually eschewing magic in modern 5E like they did back in 1E.
Also if you look at 1978 AD&D 1E, you had 11 total options (including Bard). Of those 11 only three had no spells - fighter (both subclasses had spells), Thief and Assassin. If you count multiclasses, that number is 5 non-casters out of 20 class options you could select at 1st level, so yes even back in the day casters dominated the available selections.
In 5E they can do this without spells relatively easily. IT is more difficult to do it without magic, although adventuring in 5E without magic is easier than it was in earlier editions.