I think this is a common misconception about Chien Pao - it only for sure 2HKOs Skarmory if it's Choice Band, and only with Crash, and only after rocks. It has to be Adamant Band to for sure 2HKO it with Crunch after rocks. And if it's band, then you are taking continuous hazard damage on top of Skarmory helmet damage, etc. People are kinda brushing it off as not a real check when it's a very real check - it's just not perfect. Not to mention this is only Band Pao - any other Pao is pretty well checked by the bird. And if it is band, then as long as you're not silly with hazards all you need to do is switch in Mag a couple times on it. Hazard removal is not really a spectacular thing in this tier.
Having sufficient offensive counterplay is also a very real thing to consider in weighing on how banworthy something is - and Pao has plenty of it as Bella mentioned. Also stating Tina opens itself up if it teras goes both ways, so stating that in connection with how it can 2HKO Dozo with Tera Dark Band Crunch (again only if it's Band) is kinda weird - not to mention you're going to know right away if it's band when it does this. Also it's not like Pao is the only thing with little defensive counterplay - Zacian is almost the same thing except a little less power in exchange for more Speed. Many Arceus forms have little defensive counterplay once they start Calm Minding depending on the form - especially since they can actually use more than 3 typings of moves (and usually Pao is going to use only STABS 90% of the time).
Overall, if this was an OU tier and all of these mons were OU, I still wouldn't think Pao was bannable because of the answers it has. It is most definitely not banworthy by Ubers standards (not even close). And so if we're gonna end up banning it, then we may as well put several more Arceus forms, Zacian, Chi Yu etc. all on the chopping block too and turn this tier into more of an OU than Ubers (not ideal imo bc I think the tier is very fun as it is right now)
On the fence about the ban right now but I think different tera options besides dark should be explored, especially on sd boots sets. These teras and builds kinda invalidate all mentioned checks outside of dozo, who basically always beats boots pao no matter what. I think if it was just the tera dark sets I would 100% vote do not ban, but after using other tera type(s) it feels like he can choose to beat all but one or two counters with each set he brings. A lot of the mons that you would put on your team only situationally counter is probably the biggest concern, zama beats pao unless its sword then the hp threshold is way lower, the birds beat it unless they get flinched or a crunch defense drop, dozo wins but it has to drop so much else as Leo said. All that being said it still doesn't feel oppressive, at least not oppressive enough to ban comparing it to other pokemon that did get banned. You can use the same tera argument I brought up against Zacian for example, where things that in theory should beat it lose to certain Teras. The big thing there is that both common zacian teras (fire and ground) make it weak to common attackers, while pao has the same issue, he can use things like sucker punch/ice shard to beat out jet punch or scarfers which does limit the offensive counterplay a bit. Sorry if it was really rambly its almost 2am for me but I just wanted to get some ideas and thoughts out about Pao so we can make the best decision for the metagame.