Edit: I do think your post is well thought out and good, I don't mean for this to come out too aggressive I'm just a direct person.
The first issue with your post is the premise that tanks are somehow in much shorter supply than healers. While I'll agree in PF content (so like EX+) it'll generally take longer to get a tank the only roulette I've consistently had to wait more than a second or two on lately (primarily queuing as an AST) is 50/60 which I don't do often. It's been this way for weeks now and going into 5.0 with a new tank and no new healer is likely only going to shift things further in this direction.
I play at varied times of day so I don't think I've just found some kind of sweet spot. If my normal raids/trials/experts/etc are popping instantly that means when I'm queing there is either a tank waiting already or a tank queing at more or less the same time as me. Either one points to a similar population of tanks and healers queing into casual content not some kind of large disparity that would advantage tanks in a dungeon setting.
The second issue is smaller but also more concrete - you don't need a tank for many dungeons while you need a healer or RDM for pretty much everything at cap outside of groups with really strong dps that can burn things down before the tank dies. A tank with no healer will die before a healer with no tank goes OOM from healtanking. Tankbusters in dungeons? I've taken most of them as a WHM, if you're prepared and have some kind of mitigation (DB/a dps utility) you're fine. Even without that most of them won't oneshot you.
I'd recommend you set up a pf or get some friends together and do some dungeons tankless, it's really not bad and kind if drives home the point of how unimportant they are in casual content. At the end of the day tanks are a mitigation tool for the party but with damage so undertuned... well, you know what they say about excess mitigation.