Exactly. Unlike the WabiSabi and JoinMarket protocols which allow you to remix as much as you want, remixing in Whirlpool is permissioned: You have to trust the coordinator will eventually choose you.
By the same line of reasoning, JoinMarket and WabiSabi are permissioned, because you need to trust that the coordinator or the offer makers will allow you to join their coins with them.
Right. The cost of the coordinator fee does not provide a defense against a coordinator Sybil attacking their own round since they are paying themselves.
Yes, however, if my understanding is correct, in every coinjoin implementation you'll have to trust the coordinator slightly at least. With maybe Joinmarket being the most resistant among all, due to fidelity bonds. In Samourai, for example, there is structurally enforced liquidity going into a mix, which means one coin in per mix, without mixing with yourself. That is verifiable by the client though (i.e., Sparrow), so you don't need to trust the coordinator.
If I'm not mistaken, in Wasabi you can choose which round to join. Isn't that much more prone to sybil attack?