One thing is to give players more options and more chances to have fun, and another entirely is to not care about balance at all.
Options = power creep. Allowing free rein, by its very nature, also means not caring about balance.
I'm not sure there's a perfect way.
3e, for all its forumulas and math based around bonuses was flawed. Everyone has seen abuses by playing with "the rules", like the always on
true strike amulet. And knowing the prices meant certain choices were just assumed, clearly better than the rest, giving rise to the Big Six items everyone took. The numbers were revised for
Magic Item Compedium, but mostly to provide items players would want to take in place of the static bonus items.
4e didn't really rethink magic items and just tried to solve the problems from 3e. The levels were really a more granular version of rarity, and there was some funkiness there as well. Likely for the same reasons: lots of magic items being written by multiple people who are on deadlines and didn't communicate.
The current rules require too much DM intervention, I don't want my players to relly on my whims -as there is zero guidance on what makes an item a certain rarity or how it relates to how useful they are-, even if I homebrew anything that is still my whims. I need to be sure that whatever I use is readily available to players and not subject to negotiation, using the items is the fun part, not the many hours of negotiation that led to them being gotten. And it being third party increases the chances it could be accepted when I'm a player.
"DM intervention" is needed for planning encounters, especially with terrain. It's needed for spacing encounters and permitting rests. It touches all aspects of the game. The game does not function without a DM.
You say using the items is the fun part not the negotiation. I wouldn't disagree. But getting the item should be just as gun as using it. Crafting items is bland and not particularly fun. Not compared to adventuring to find a desired item.