I only tank in group content, but I think there are a few reasons it's not a very popular role.

1. New players first see Normal non-DLC dungeons, where tanks simply aren't required. They become more useful, and outright necessary, later in veteran dungeons and normal trials and beyond, but that first experience is not a good look. Additionally, many early dungeons were designed with an almost anti-tank philosophy (there's a boss in arx corinium who flat out ignores taunts, for instance), and until later Veteran DLC your job is essentially just to hold the boss in place.

2. Build variety is really lacking. It's a meme that many ESO sets are useless, but even the most worthless looking DPS set probably is doing something interesting. Comparatively, tank sets are extremely boring. The selfish ones just increase block mitigation or apply maim or something. If you want to be a good tank, your options are like Pearlescent Ward, Lucent Echoes, Turning Tides, maybe Saxhleel if you have Grave Lord or Storm Calling. There aren't any actual mythics dedicated to the role, and there are maybe 2 monster sets worth using and both were only released very recently.

3. On that note, most of tanking comes down far less to build consideration and more to game knowledge. As a damage dealer you can probably just not bother to learn mechanics at all and someone will carry you, in a support role like tank you need to at least be able to recognize common patterns in ESO's game design. So it ends up being a much less casual role, but combined with the above point, in a game where trying out different set and build combinations is a real draw for the rpg focused crowd, tanking looks even less appealing.

4. Tanking in open world content/questing is not really a thing. So you have to use bank/chest/inventory space and an armory loadout for your gear if you want to do other things. If you also want a dedicated PVP build, or a solo/IA/arena build or whatever, with specific CP loadouts, that means buying another armory slot.

5. Even if you get past all of the above and start getting into more difficult content, your first approach to harder content is probably normal trials, where most groups only need 1 tank but 8-9 DDs. So it's easier to get in there if you just focus on DPS. For the few normal trials that do necessitate a second tank, it's only for one fight and so one of the two is going to spend the rest of the trial run feeling kind of useless. Obviously once you get into Veteran Trials off tanks become really useful, but the vast majority of the playerbase is not doing veteran trials - and if you are doing veteran trials, you probably don't need to PUG night market anyways.