Shellder doesn't overcentralize teams. Checks are present and very capable, and its often pretty clear to both players what needs to happen in order for Shellder to win the game. It doesn't force specific Pokemon on teams, you were going to run something that's likely a check to it in some form anyway.
I agree: most teams would run a Shellder answer anyway, but that doesn't mean it can only be used to check shellder through the whole game, this ignores the fact that the opponent has other five Pokémon.
Your Mienfoo will have to check a lot of your opponent's Pokémon throughout the match and could be knocked or chipped, but it will die to Icicle Spear after rocks, but it could also be Tera Water Liquidation.
Your Mudbray (That you need to tera btw) will be chipped by a Vullaby, Stunky, Diglett, Glimmet or Elekid;
Your Foongus should live Rock Blast if you keep its Eviolite, but what if Shellder is Icicle Spear?
Your Mareanie should live Rock Blast if you keep its Eviolite, but it cannot get knocked, and well, if Mareanie is your Mienfoo check, it's likely to get knocked during the game, but shellder could also be Tera Rock or Ground Blast.
Your Chinchou could get chipped by Elekid and Vullaby.
It does limit teambuilding in one point; that being defensive tera, but this isn't a huge problem overall.
Priority is present pretty much everywhere in the tier, and the two best users of priority still completely stop the clam.
What would those be? Stunky and Mienfoo? A-Diglett? A-Sandshrew? I assume you are talking about Grookey, the one with the least usage of those. About Grookey, it's not really a good Pokémon and Glide doesn't even kill Shellder at full HP and -1 Def, and is also bad against Ice Shard. On Stunky, you can't just say it "completely stops" Shellder, because it simply doesn't; Not only Shellder can live Sucker Punch depending on how much HP it has, but it also can run a Fairy Tera, Substitute, Ice Shard, run a more bulky set and of course win the 50s.
Shellder fails to score many key kills without tera, which means that you're either chipping down several pokemon in order to have a chance to sweep a game.
I also don't think this is true, since it can KO Mienfoo (with rocks up), Vullaby, Foongus, Mudbray, Toedscool, Elekid, Glimmet, Stunky, Diglett-Alola and Gothita, while also being able to 1v1 Sandshrew-Alola and even live an Earthquake at -1 when it tries to revenge kill Shellder most of the time. Out of the 15 Pokémon ranked A- or higher, it can beat 11 of those with little support, no tera and a common moveset. (Other Pokémon are Mareanie, Tinkatink, Chinchou and itself)
The variety of options that Shellder has is vastly overrated. At the end of the day, Shellder has 4 moveslots and a tera slot. It cannot block Fake Out with Tera Ghost and score kills with Tera Water. It can't run both Ice Shard and Protect. Reading what Shellder has is also incredibly easy. You'll see these random arguments that Shellder can do all of these things on paper from people who just don't see the game at a high level. Admittely, sometimes the exact tera or the 4th move can be a little ambigous, but frankly the endgame line doesn't really change.
I personally don't like the argument of "you can't predict what is Shellder's set going to do because you aren't playing at a top level" but if it matters; at the very least tazz, kythr, Colin, Éric and myself (5/7 in the council, not sure about Laroxyl's and Hacker's takes) have the "if there's a Shellder, there's a way" mentality while facing one, basically meaning that we can't be sure about its set, and usually go through weird endgames, like "This wins if it's Liquidation but loses if it's Ice Shard", where there isn't and option that covers the three or four most used sets.
Shellder promotes healthy resource management
It's healthy if you know its set, but since we don't, the safest way is keeping your tera to answer Shellder, which creates an unfair dynamic — I can't use my mechanic until my opponent reveals their Shellder set, but they might have positions where teraing another mon will make huge progress, or your tera being useless against Shellder anyway (like Steel Foongus against Rock Blast, Liquidation Protect Shellder or Tera Blast Ground)
If you're not convinced, take a look at every Pokemon you think is banned because of Tera, and ask yourself if it's because of defensive tera or an offensive tera.
Banned Offensive Pokémon where Defensive Tera had a huge impact:

Scraggy, who clicked tera poison to setup Dragon Dances;

Snivy, can argue it's both offensive and defensive but clicking tera poison and substitute on a Foongus to wall its moves isn't really what we mean by offensive tera;

Magby, The Belly Drum Tera Ghost set — the one who got more people to agree on its ban — is both offensive and defensive, but I also would like to mention this
one game where I only won because of special Magby using tera Psychic defensively.
Banned Offensive Pokémon where Defensive Tera hadn't much impact:

Eviolite sets could run tera Fairy but that wasn't really relevant for the ban by itself. (that set might've also been considered healthy by people at some point?)

Didn't matter.

Tera fire was a good defensive resource in Sandshrew-alola matchups but it was mainly to KO Foongus, Tinkatink and other Voltorbs.
Banned Offensive Pokémon where Defensive Tera was a decently relevant factor:

Tera Ground Blast was the most broken part, but it being able to setup against Mienfoo and Tinkatink's Thunder Wave was an important factor as well.
Suspected Offensive Pokémon where Defensive Tera had a huge impact:

Gothita was suspected mainly because of it's defensive tera set — Steel/Flying to setup against stuff it shouldn't.

Shellder also makes good use of defensive tera to setup, specially Ghost, Fairy, Rock and Ground but also Grass, Electric and Steel.
Legal Offensive Pokémon where Defensive Tera has a huge impact:

Sandshrew-alola's primariy set is tera Fairy, mainly to be able to wall Mienfoo (and live other stuff it shouldn't) and KO or Setup in front of it.

Tera Ghost Vullaby to live Fake Out is a classic, but we can also mention tera Dragon and Ground to live a hit and 1v1 Electric-types.

Tera Steel Sub SD set is also a classic and we know how much it auto-wins against many Foongus teams.
Legal Offensive Pokémon where Offensive Tera has a huge impact:

Tera Blast Ground sets to nuke Glimmet and Tinkatink.

Many options, like Flying, Ground, Stellar, Dark.

Again, many options like Psychic, Grass and even Ice.

Usually Ground to KO Chinchou, Mareanie and a chipped Tinkatink.

Tera Fire to KO everything in the late game.
You could argue that some of those Pokémon use their defensive tera to setup so it ends up being offensive after all but I disagree, in fact I don't think that offensive or defensive tera are much different, since both have the same purpose — beating stuff it shouldn't.
Example 1: You click tera Water on your Mienfoo at 50% against a Scarf Growlithe and KO it with HJK.
Example 2: You click tera Steel on your Foongus against a Shellder and KO it with Giga Drain.
Example 3: You click tera Psychic on your Elekid against a Mienfoo and KO it with Psychic.
Example 4: You click tera Ground on your Shellder against an Elekid and sets a Shell Smash.
I assume you would consider the first two as defensive, the third as offensive and the fourth as both, but as you can see, in the 4 examples, your opponent is the one with the momentum — 1- Your Mienfoo dies; 2- Your Foongus dies; 3- His Mienfoo lives 4- Your Shellder Dies — but with Tera, you nuke their threats and shifts the momentum. The only difference is:
who's attacking first, but the tera user's goal is always the same — shift the momentum by nuking the opponent's threat
. If that's the idea, the Offensive pokémon running a Defensive tera, so it lives the opponent's moves and therefore click a setup move to be able to beat it, shouldn't really be considered offensive, because they are not threatening an imediate KO.
I'll likely vote Ban on Shellder.