One thing about "unified mechanics" is that it is a bit of a fallacy in current D&D.
Rolling d20+mods once to see who "wins" a skill contest is different than rolling d20+mods then 1d8+5 for damage, then rolling again until you run out of HP (or rolling initiative etc.), and also different form rolling nothing but MAYBE letting your enemy roll a saving throw.
D&D has three types of checks: attacks, saves and ability rolls. Not to mention spells. They all work slightly differently. A "natural 20" only matters in combat, for example; this isn't unified.
Also... there are very few games that resolve a 10-minute combat with a single roll, but many will resolve other 10-minute tasks with a single roll.
In practice, this means a 5th-level wizard can never, in a million years, beat a 5th-level fighter in a sword fight, but the fighter will beat the wizard's arcana check about 10% of the time (or something like that).
Many times, "unified mechanics" are a illusion.
With that said, the more truthful feeling of "I like to use the same dice for everything (except damage because we are used to that)" is okay too.
Also, IMO, in practice, a bell curve works best for skills, but it is very boring for combat. I noticed that playing lots of GURPS and D&D. Ultimately, I chose to play modern D&D as written, just distributing lots of automatic successes to circumvent the obvious flaws in using a d20 as outlined above.
The thing is that even the idea that in unified mechanics every single roll in the game has to be made in 100% the exact identical way 100% of the time is itself a fallacy. It places an extreme standard on what can be discussed as "unified mechanics" and I've never seen anyone argue in favor of that, other than people arguing against unified mechanics or making some criticism of them. So it's basically a sort of straw man and reductio ad absurdum, because it argues against something nobody is arguing in favor of and attempts to dismiss or at least find flaws in the method by appealing to extremes rather refute the mechanics on their merits.
And in all of the types of checks used in D&D, the resolution method is still basically identical (at least in 5e), and all of the differences are superficial and either D&D conceits (D&D has used different damage dice for weapons and critical hits for most of its history, and saving throws in response to spells, and critical skill rolls do exist in other games--the designers simply opted to not include them in D&D) or circumstantial differences that arise naturally in the situations they're implemented (you don't need to hack away at an enemy's HP or "life meter" or whatever in a crafting skill check--because they deal with completely different circumstances that have different end goals and obstacles). But because I'm not hacking away at an enemy's HP when making non-combat skill rolls I can't talk about how attack rolls and skill checks are rolled in 100% the same way anymore?
In D&D 3e they introduced the idea of handling all rolls involving some type of ability tests using a d20 + Modifier mechanic, but they used different methods to determine the modifier for different resolution rolls (combat vs saving throws vs skills) and kept weapon damage rolls, rather than ditching that staple of D&D in favor of automatically determining damage based on your attack roll result. Does that mean I can no longer recognize the elements of mechanical unification that are there compared to earlier D&D?
Even if you want to argue that unified mechanics exist only in degrees the elements of unification are still there.
I agree with most of what you're saying.
Would you agree that there are "degrees" of unification then?
On one hand, you've got OD&D - roll high, roll low, roll 2d6, roll 1d00, roll damage.
OTOH you've got WotC D&D - roll 1d20 for almost everything, but occasionally add bless, bard inspiration, roll damage, consider critical hits, etc.
Then you have games that are MORE EXTREME than modern D&D - like Robin Law's Heroquest, where everything actually uses d20s and no other dice are used. Or Fate, which uses nothing but fate dice.
My question is: do you think unified mechanics are always good, or are good in general but can be left aside for various reasons?
(such as "D&D has used this for most of its history", or "they deal with completely different circumstances that have different end goals and obstacle").
From your post, your answer seem to be, obviously, that they are good in general. I agree. But there are exceptions - and these exceptions deserve to be analyzed on their own merits.
I don't think "D&D always used damage die" is a great reason, but I see your point (I, personally, do not use damage dice in my game anymore, so in this sense my game is more "unified" than mainstream D&D in this regard).
Here is another obvious one: combat is completely different from skills, why should a skill be decided with a single d20 roll?
2d10 works best in practice (for example, the fighter beats the wizard in Arcana about 1% of the time instead of 10% of the time).
Again, in practice, I decide in favor of unified mechanics here too - but I would understand if someone decides otherwise becasue they want results to make more sense.
In short: "unified mechanics" (which I prefer to call "multipurpose mechanics") are also just a tool at your disposal. A tool I love, but not always the best tool for the job.
EDIT: BTW, here is a fun example from 5e: thirst and hunger are treated in different ways (for no discernible reason)... So, "unified mechanics" is not necessarily a top priority here, "using the d20" might be.