I just want to give my thoughts.

1. It's only easy if you are geared similarly to the dps/healers, if you are geared under it can be a nightmare to hold hate, or even just downright impossible. But regardless, I enjoy tanking, even if you are just stood there most of the time.

2. Then fight harder enemies. Of course something like Ifrit HM is going to be challenging when you are fresh level 50 with your AF armour, but once you gear up, it's going to be a cake walk. But how can you address this? You can either make harder content easier, requiring you to need lower gear, so all the fights are tuned to your AF armour. That then leaves no room for gear progress otherwise you would start curbstomping the enemy. The other thing would be to make the bosses harder, but that then restricts the access into endgame for the fresh level 50s. They would be expected to grind out higher levelled gear straight away, just so that they can even stand a chance. As it stands, as long as you do the content that your gear level was designed for, it should still pose a challenge.

3. Considering there is a lack of tanks to start with, why would that make tanks roll DPS? Tanks are generally the most sought after and quick looks through PF can show you that when they have all slots filled except the tanks. That should in theory make more people want to play tanks as the need is there, but it doesn't. You also have to take into account the vast majority of the players are DPS. If you can replace one of the less needed tanks, which is a hard slot to fill, with a DPS, which is an easy slot to fill, you are going to. In the short of it, tanks can easily get into content, but DPS struggle more. There is no logical reason why a tank would start rolling on DPS/healer and in the same case why a DPS wouldn't go as a tank.

As for battle fatigue, I honestly don't like the idea. It is essentially a forced tank swap, but applied to all content. Ok, so it might make some fights without a tank swap, actually require one, but what about the fights that do require one? Would you tank swap based on the fatigue, or the actual tank swap debuff? If you get forced to switch on the fatigue, then who's to say that won't mess up the tank swap debuff? If you get forced to switch, but the debuff timer hasn't worn out yet, you then get smacked by it, increasing the timer and needing to swap again for that, but the other tank hasn't recovered yet, that's a bit of a bind you are in. 2 tanks who really shouldn't be tanking, not a good idea.

So, what if you switch on the debuff? Well then, what's the point of the fatigue to begin with if it doesn't change the fight? Adding to that, if you do make it so that tanks can recover more than their initial state as it were, then it makes the fight even more trivial. Assuming you recover quicker than the main tank, so that you don't end in a position where both tanks get slowly worn down as the recovery isn't enough, that then leads to the position that the tanks will be taking less and less damage the more they swap, which brings us to your second point where you have already stated that things do too little damage in the first place, and what you suggest makes tanks take even less damage over the course of a fight.

Overall, there are several problems with your idea of a battle fatigue, mainly focused around tank swap mechanics already in the game, and that's without even giving specific examples, one big fight where I can imagine battle fatigue would be the worst is in the case of Titan Extreme. Adding Vulnerability up and then naturally increasing the damage you take just for being there isn't going to be fun, especially for the healers.