Depends highly on how it's implemented.
Sure, having an unidentified items adds some amount of tedium; having to use some means (usually consumables) to identify things, possibly wasting said consumable if the identified thing turns out to be worthless. Sure, it's nice to know that's a potion of poison, but I'd rather I hadn't wasted a scroll on this worthless item... etc etc.
Of course the identify-minigame will be done and obsolete by endgame.
But you lose so much by removing it!
If all potions are identified, you might as well remove all negative potions. Players will probably never pick them up, so what's the point of their existance? Sure, you could throw them at monsters, but how many of you actually do that?
If all scrolls are identified, you'll definitely be deleting scrolls of curse X, amnesia, aggravate monster, summon monster etc etc. Monsters won't ever read them, and the player will never pick them up, so delete them from your game.
If all equipment is identified, there will never be equipment with negative modifiers, or cursed equipment; people just wouldn't pick it up. (you could balance THIS point by making cursed weapons very powerful, or combining strong positive modifiers with strong negative modifiers...) Therefore you'll only have two sorts of weapons in your game; vanilla weapons and a spectrum of positively enchanted weapons. Same applies to armor, rings and the like of course.
Simply to get rid of the tedium/consumable drain of identifying items, you've gone and made your game dull and boring!
Of course these are generalisations. I like FayAngband's system where equipment is identified automatically, and you receive a free identify via (p)roficiencies every time you change floors (there's also a system where your minimum floor depth goes up every time you change floors so you can't abuse this). Sure, nobody would every pick up a sword with -X modifiers, but who doesn't hate equipping something and feeling that deathly chill? But you still have the excitement of identifying all the other things.
These mushrooms, what could they be? Do I waste my once-floorly id on them, or do I just eat one?
What will I id this floor? That scroll I found last floor, or hang on to it in case I find something potentially more interesting?
What could this Staff be for? (Like unwrapping a christmas gift, finding out what magical tools do
)
Another example of a game doing things interestingly is Incursion. Identifying items was done simply by reading scrolls of identify, but the player also had the chance to spend several hours (a couple of hundred turns ingame, if I remember correctly) and some fatigue points (regained almost only by sleeping, quite dangerous to do since it refills the monster pool on the floor) in a skill check to
try and identify something.
Of course there was the chance to fail, in which case you could not use the same skill on that item ever again.
That's nice, but the real fun part was cursed items. On the second floor (and with a small chance of spawning on other floors) there was a library filled with spellbooks. Being inside of the library room allowed you to do a skill check on researching the curse on an item, to try and lift it.
And
that could be an interesting way of handling identifying items. (Of course, it does add the tedium of having to lug all your gear to the library so you can start identifying all of it and deciding what to keep/squelch)
In closing, there's plenty of things that can be CHANGED about identifying things. Some things could stand with being auto-id'd from the start of the game, and possibly
the way in which the player is able to id things (whether we're talking scrolls, id-by-use, once-floorly proficiencies, divine intervention, doing research in randomly spawning libraries etc) can be changed in favor of fresh gameplay.
But to outright remove the need to identify things completely would make a game lose far more in the fun-n-flavor department than it loses in the tedium department.