Yeah unless you make very certain an item is only usable to a given character or specifically gifted to/earned by them in game, if you find magic items in some old ruin, the party will figure out on their own how they are divvied up.
My take is not to worry about "balance" but just give items to the person they would be more useful for. This usually means I have less items than other characters, but if I'm a Wizard, I'm not going to say Bracers of Defense should go to me over the Monk. Ironically, this actually happened in a game I was in where a Broom of Flying came up.
I suggested it go to the Fighter, but he "didn't want to look like a sissy riding a broom", lol. So it went to the party's archer instead.
Then we got into a fight with some flying enemies and the Fighter was annoyed he couldn't use his Sunblade and had to switch to his non-magical bow "God, my damage sucks now!".
While it's true that magic items were used to balance classes in older editions, and could be used to balance them now, I think putting them back in the DMG instead of allowing them to remain player-facing sunk that ship.
People may not like "magic marts", but with no ability to determine what items they are going to want/need, it's now solely up to the DM to figure out how to use them, and they are given basically no guidelines other than-
Item rarities, like these things are MtG cards, and "make sure you don't someone have more than 3 cool items, that might wreck your game!", which is a truly ridiculous rule.
Limiting how many optional things your character might acquire when it's entirely up to the DM to determine how many of these optional things are even available to you? Come on, now.
That makes as much sense as the 2e Paladin not being allowed to own more than 10 magic items ever, and having a class ability to allow him to use a Holy Sword he might never even see in play.