Thresh is distinct and unique, and because of it all the supports have lately have just gotten so much better, but people just cry fowl because a well designed champion is popular?
Define well designed. Being able to do everything your role would want (explanation incoming) isn't well designed. Part of the design philosophy of League is the state of perfect imbalance...
https://www.youtube.com/watch?v=e31OSVZF77w
and thresh does not exhibit that at all. In the cyclical imbalance that league is designed around thresh can counter any champion picked against him because he has tools to deal with them all. All in supports are weak to poke, poke are weak to sustain, and sustain are weak to all in. Thresh has his shield and naturally gets a relic shield so he has sustain, his hook and the damage amp work as poke, and the 2x cast hook as well as his flay work for all in. He exhibits qualities of all three categories. This means that if played into the match up correctly he can always come out ahead through sheer diversity of tools in his kit. Each of thresh's abilities are somewhat underwhelming, but when put together create a kit that has little in the way of actual exploitable weaknesses.
Isn't the point of a new champion to be something people want? Playing as Thresh, and playing against Thresh are both meaningful scenarios, he can fluidly execute his moves to achieve his design goal, but even when he does so, there is something the enemy team can do in response to every one of his actions.
What is his design goal? You have described it as single target lock down but I've demonstrated clearly that his kit is not focused around that, and there is not something every champion can do to counter every one of thresh's moves. Thresh has the tools to counter anyone, which means he is safe to pick in any match up.
I had initially addressed each of the champions you listed but found that the above argument was more clear and concise. In any case i typed these up and didn't want that to be for nothing.
That Blitz point is absolutely fair, that is how most Blitzcranks play. However, successful Blitzcranks use their move speed boost to get onto one target, knock them up, and save the pull for when the enemy tries to use their escape. Sounds like single target lock down to me. Meanwhile Thresh has great single target lock down but can also disengage the fight, shield and protect the adc, peel, poke. Blitz lacks so many tools that thresh has it isn't even fair to call thresh a single target lock down champ compared to Blitz. All blitz gets over him is a better hook.
Leona may be scary, but she has no poke and no sustain. Her kit is built to go for all in trades and she lacks in other areas. She is good at what she does but lacks the tools to do everything. Thresh may not be able to all in like Leona, but she can't poke or shield her ADC.
Braum has peel, disengage and anti-poke but lacks all in and lacks sustain. His kit lacks in distinct areas. He is strong at what he does but lacks tools he shouldn't have. Thresh may not be able to block projectiles but that's really all Braum has, Thresh still saves carries better than Braum could dream of and doesn't have to risk getting caught out to do it.
Tahm has poke and a little sustain, but he has a hard time going for the all in because he lacks gap closers. His kit is very vulnerable to kiting. His kit lacks in distinct areas and doesn't have tools to do everything. Tahm has better disengage but Thresh isn't near as kite able as tahm.
Thresh can do everything each of those champions can do. With poke, disengage, engage, shield, peel... he just has more tools at his disposal than every other support, even the champs you listed, and that is what makes him such a contested pick. You know that no matter what thresh will fit into the team comp your team builds while with these other picks you run the risk of lacking tools your team needs.