I like this. At the end of the day, casters get the equivalent of magic items through spells.It seems like your objection is that because the rules for such a feature could be poorly designed, nothing even similar to such a feature would ever be worth attempting. That smells like a fallacy to me.
Here's an simple suggestion:
At 11th level, and every 2 levels thereafter, the fighter can choose a rare item. At 17th level, the item may be very rare. At 19th, it may be legendary. Flavor as desired.
Not exactly a crazy page count, nor did designing it break my brain.
Although, given the page count that some spells take up, one big fighter ability that requires a page (or, gasp, even two) doesn't strike me as all that unreasonable.
Fighters can get this opportunity through the meta. Say every x levels the DM asks for a wish list from the fighter that can include items up to y rarity. The DM then makes available an item to the fighter from that list (or something substantially similar). Easily explained in game as fighters are often fate magnets etc. Nice easy way to keep up parity and give the fighter more cool options.