They should recuse themselves from any vote involving an industry that they have a more than trivial amount of stock in. Do you expect someone to restrict Big Tech when they have Facebook and Google stock?

Absolutely not, we are talking about politicians here. I like the idea of divesting into index funds during time in parliament / service.

If some Congressperson went short the market and then tanked the market though some statement that would indeed be very bad! Has anything like that ever happened? That would presumably nuke that person's reputation with costs far greater than whatever financial gains could be had.

If they're long the market and then boosting the market... I mean, isn't that what we want? You'd have to go further than a blind trust even and ban owning equities at all.