A while back, the design philosophy for supports was that they had to offer a broad enough range of CC and/or utility to compensate for the fact that they had little to no scaling, which led to "do-everything supports" like
,
,
and
. This was also the first champion designed by CertainlyT that truly had a lot of different effects on his kit, and it's likely the design team was OK with giving him as much stuff to do as he has now. Changes to the meta and to champions ended up favoring tank and peel supports, which is one of the reasons why Thresh, who can do both really well, is so prominently picked.
I agree that Thresh has too much on his kit, and arguably he covers multiple niches at once, while never truly suffering even in the worst matchups or comps (he always has at least one good answer), Overall, I think the issue comes from him being able to poke as a tank, and being able to offer defensive utility while having a kit that mostly focuses on engineering hard-engages and locking people down. If he were made melee and had his poke and defensive utility stripped in favor of better damage, CC, etc., then he'd have a solid niche and remain popular without being overpicked.
What's also important here, though, is that Thresh isn't the only support guilty of having an overloaded kit; he's just very prominent due to being one of the most played champions in the game (also likely for being a CertainlyT champion). A lot of other supports lack a well-defined niche (seriously, what is Nami's niche?), except a lot of them aren't as hated because they're not as popular.
has point-and-click CC, AoE defense bonuses and a heal, plus fairly decent damage, but is just not that good to play most of the time, Sona's got access to literally ten different effects on her kit, but none of them are prominent enough to make her a popular competitive pick most of the time. Even
, who's mostly peel-oriented, occasionally becomes too good an offensive pick, though unlike Thresh she keeps getting nerfed when that happens. Supports likely need a pass on their kits to give them stronger niches, and ideally that should mean Thresh should eventually have a less overloaded kit.