Yep, these are great points. There is no way to punish signing the wrong thing directly, just not changing your answers without risk to funds.

One of the interesting things is that upon a single equivocation you get unbounded equivocation by 3rd parties, e.g., you can completely rewrite the entire signature chain!

Another interesting point: if you use a musig key for your staking key that is musig(a,b,c) you can sign with a until you equivocate once, then switch to b, then c. Three strikes and you're out! IDK what that could be used for.

Lastly, while you can't punish lying, you could say "only the stakers who sign with the majority get allocated reward tokens for that slot". So you could equivocate to switch and get tokens, but you'd burn your collateral for them. But this does make an incentive for the stakers to try to sign the "correct" statement in line with peers.