Des I would argue that it is only the most underplayed tank because it has the least dps and soloability out of the tanks... which is fine. It is a tank class, and it is not supposed to deal massive amounts of dps (and arguably also should not be able to solo well - see: social, group-focused MMORPG). This class is insanely good as it is right now, and you didn't even point out one of the few major reasons why...
Purifying Blow. This, now that there are significantly less ways to Purge enemies of their buffs compared to months ago, has become an absolute must for any serious group in certain situations. This skill alone will speed up your TTKs, reduce your downtime (if you even have any) due to Mana constraints, and subsequently raise your group's EXP/hr rate through the roof. Combined with everything else they bring to the table, the class feels fantastic in groups, especially against caster-heavy camps (and the raids that are currently disabled).
It isn't even close, in my opinion, that the Inquisitor is the best actual tank in the game because of the additional utility and control that they bring (notice how I am not focusing on dps coming from my TANK). If we want tanks to be able to slot into dps roles, that should come in the form of stances of some sort that actually reduce their capability to tank and their dps should not be comparable to an actual dps class. And to make note about sustain tanks - this should really be a limited capacity if accompanied by the dps capability an SK brings, or made into a primary function of the class as it is the case for Paladins. You should not just be able to solo your way efficiently through the entire game - there should be good reason to want to group, and part of that reason for people who choose to play tanks should be that grouping makes your efficiency while leveling significantly better. If everyone could solo efficiently, why would they ever want to group? But, this is digressing into the other design flaws the game currently has, and is getting away from the point at hand - how Inquisitor fills it's clearly defined function well, and why changing much about it from the current iteration w/could be bad in various ways.
Thinking that Mana Burn and Mana Drain are useless is certainly a take of all time. Both of these are insanely useful and neither of them leave my bar, and I use them all the time (see above - if you ever have Mana issues, it is because you are not utilizing these in conjunction with Purifying Blow vs mobs that are buffing themselves).
Thinking that Mez is bad/impossible to accomplish in a fight is also insane, especially when you compare it to Root. Mobs can use tons of stuff at range (shoot, spells, charges, etc...) now. This comment alone makes me think you have not played the game in a long time, or you really just don't use what is available to you. 15 Mana cost to completely nullify a mob for 30 seconds is absurd value, and tbf if you are getting interrupted constantly, you either a) are not pulling properly, or b) are not using your abilities properly. If you are the puller yourself, you need to pull better... if you are not the puller, you can freely Mez mobs as they come to you/your camp. Even so, if you DO have multiple mobs on you, you can use the Scintillating line to Stun them all, then tab through and Mez.
Having the worst soloability in the game is fine - tbh this should be the case for many classes, since this game is supposedly being designed as a social MMORPG. This isn't Skyrim.
And yes, spell-specific shields are part of why the class is unique and good. This is something that other classes do not specifically get, and as such give reason to your group as to why they would want to slot an Inquisitor over any of the other tank classes. I am taking an Inquisitor, personally, over any of the other tanks in the game, if I get a choice in the matter, solely for the additional crowd control and the spell damage mitigation they bring.
You must be a pretty low level and surely are not focusing on INT if a single nuke is taking up to 20% of your Mana. I think you could change your gear around and level up a bit and your tone might change on a lot of your takes here. I will admit that the soloability is bad, but that in itself is not a bad thing. Again, that encourages group play, which is what MMORPGs are really about.
The Inquisitor is an anti-spellcaster disruption tank. It's entire kit revolves around that, and it performs that function superbly. If we start talking about taking things away from the class, I agree that some things that overlap from the Enchanter could be taken away (buff utility being probably the only thing I would say makes sense here, since crowd control via Mez and Scintillating lines fits into "disruption tank" quite well)... but if we want to talk about overlap being inherently bad, then we need to change literally all classes... and not by a small amount. Every class has overlap - the question is, are changes being made to classes right now because of that overlap (and their potential desire to reduce overlap), or are they attempting to make classes functionally unique (while allowing some overlap)? That's where the distinction comes into play with regards to applying this conversation to the Inquisitor, and is exactly why they really don't need to change the Inquisitor very much, if at all - the class is already the most unique class in the game, and it performs it's intended function extremely well with the kit it currently has.