With multi-attacks and accuracy already being quite high, a +1 to hit is generally worth less in 5e than it was in 4e.
(Unless you're a rogue. Maximising acccuracy is something a rogue should always be trying to do the maximum extent possible).
Sure, though you could just leave daggers and other Rogue weapons out from that particular benefit. Since it specifically requires "a finesse or ranged weapon," it's simple enough to just say that that particular tag should not be used at the same time as the finesse tag, and is melee-only. Then you could have a 2d6 "precise" greatsword and a 1d12 "high crit" greataxe. You could even the maul bring back the "brutal N" tag, meaning every damage die rolled for that weapon must do more than N damage (aka "if you roll N or less, reroll it until it's more than N"). So you could have a 2d6 brutal 1 maul (average 6, 12 on a crit) compared to the more accurate but more variable greatsword (average 7 damage, 14 on a crit) and the more devastating but even more variable greataxe (average 6.5 damage, 19.5 on a crit).
This would have the side benefit (for those who see it as such) that axes and mauls would be more favorable to Barbarians and folks
not using Great Weapon style, while those who do use it would favor the more expensive greatsword. Their ways of fighting would thus naturally lead to them using the associated weapons.
I agree it would not break bounded accuracy, but I also think it adds needless complexity to the game, more stuff you have to keep track of.
It seems to me that the overall average opinion is that 5e erred on the side of caution when it came to complexity. That's why we have things like Level Up. There's a sizable market for "5e, but with a
bit more crunch." (Honestly, there's a sizable market for "5e, but with a pretty fair amount more crunch," but I'm fairly well convinced WotC at the least doesn't think that market is worth the opportunity cost of chasing it.)
Also, you make it sound like these things are huge overhead. They aren't. They literally match existing rules in various ways. Officially list them as optional rules if that's what you need, but come on man, if the existing Fighting Styles aren't "needless complexity" then these weapon properties can't be either. It's literally: "increase your +hit by one," "roll 3x your weapon dice on a crit, not 2x," and "reroll all damage dice that are too low, until they aren't." I mean, for goodness' sake, the Champion--that is, the simplest subclass of the simplest class--gets
two Fighting Styles, and I've literally never seen anyone complain about that being burdensome overhead or needless complexity, despite many of them being
more complicated!
I get, very much, that there's a contingent of 5e fans for whom this edition is at the ragged edge of tolerable complexity, and it sounds like you're at least sympathetic to their position. But those fans were never going to be the primary focus of 5e's future development. WotC wants to sell books, and make every book so that it offers DM-facing material
and player-facing material so that everyone has a reason to buy. They were never going to take a policy of "never increase the complexity, but maybe decrease it now and then."