I think a lot of stuff is getting lost or obfuscated here, so I want to bring it back to the start.
The initial idea was, a tank defensive that reduces the tank's damage in some way in order to use a defensive action.
The first thing we need to ask is why? The tank role has never had the expectation of reducing their own damage in order to increase their own defence, except maybe in the early days of the game where tanks used tank stance. Getting towards the end of Final Coil, tanks did start using DPS stance when tanking but it didn't really catch on until HW where it was expected of tanks to use DPS stance, especially when you had WAR and DRK who were 2 powerful tanks that were fully capable of doing so. From then on, it has been DPS stance all the way through, including SB. This distinction is now no longer present.
This is one reason why I say it is a bad idea. It isn't something that has been drilled into people from the start and so adding it now is just going to cause backlash. You mention simplifications escalate, yes, they do, however, this is something that has been simplified from the past, this is just how it has always been.
Onto the next point. Why does the tank have to sacrifice their own damage for the potential for a healer to gain damage? No other role or job in the game does this. You can say a healer might have to waste a GCD on healing to save a DPS from dying, but that has a much higher tangible reward to DPS and it is expected of the healer to sacrifice some of their damage for the betterment of the group. It has never been the case for tanks to do the same. Even if we were to assume tanks did have that responsibility, you cannot guarantee the healer takes that chance, which then leads to a raid damage loss and you have reduced your own DPS for the potential for more damage, but it wasn't taken. I can compare that to raid buffs. In theory, you put out a raid buff and everyone else has the potential to utilise it. However, there is the potential someone does not, which is obviously bad, however, I have not sacrificed my own DPS to get the raid buff out there, it is down to the other player to make use of it.
Again, gong back to mitigation kits. Tanks have these tools that can use to mitigate damage at no cost to damage, why suddenly add something that does? For something 'different'? Maybe, try different defensive means to make them more exciting rather than reducing the tanks damage first. This will make tanks feel more unique and it won't be a button you want to avoid.
Going to fight flexibility, I don't see how the idea comes into this at all. You say it reduces fight flexibility, but the only way that can happen is if you throw several hard hitting attacks in sequence where your defensives cannot cover it, which also then implies this damage reduction is readily available fairly frequently. However, if you go from a fight like that to a fight where there are less hard hits and your normal defensive kit will suffice, this second fight will likely to be favoured by not only tanks, but healers too, as they have their own cooldowns to worry about as well. This is before the fact that, if healers do run out of cooldowns and have to resort to GCD healing, it gets rid of the initial benefit you set out to achieve anyway. There is a reason you cannot just spam out tank busters, or constant raid wides, it just isn't fun.
How the healing kit currently operates, or potentially operates has no implications as to whether a tank's mitigation tool should or should not reduce said tank's damage output. I have said it in this thread, healers should be rewarded DPS wise for their GCD healing contribution (as, again, forcing a healer to GCD heal isn't expected unless in high end content, so people will want a reward for it). Which is also funny because if you want healers to GCD heal more, by reducing the tanks damage for mitigation, you heal with a GCD heal, which is another way the benefit isn't taken advantage of.
Again, it might have worked in the past, but it just will not work now.
This, on the other hand, is what is missing from tanks. The potential to feel like a tank by protecting the party and not just necessarily just by popping your raid wide mitigation. In wild Charge, you take an active role in mitigating damage by not only your own defensives, but also in your positioning. I have also stated a few times how CC could be used to make fights more interesting by having them change how boss attacks work. There are plenty of things than can be done to make a tank feel like a tank without having to resort to reducing the tanks damage. If you want to point out simplifications to the game, you should be concentrating here, where it matters most. The tank gameplay.