If I'm some rich dude, I could totally murder my wife, so long as I convince the jury I won't get married again.

I think they could make more general inferences than that.

And "whether or not they are found guilty" basically means you could jail anyone you feel like off the street, provided you can convince an insurer that they're dangerous. Since they'll be in jail,

I think I might have been unclear about how it would work. In order for someone to be jailed, you wouldn't have to convince just one insurance company; you'd have to convince them all, even (appropriately capitalized) mutualist agencies the person belongs to. Insurers wouldn't have any more power to put you in jail than they currently have to prevent you from driving: they can only decide whether their company will insure you, not whether all companies will refuse to insure you.

As I imagine it, jail wouldn't be something anyone specifically imposes; it emerges out of the combination of your high estimated risk level and your inability to afford insurance except when confined to a secure facility. (And, of course, depending on the society, insurance could be subsidized out of tax revenue so that the poor aren't automatically locked up. In a way, governments already vouch for the poor, it's just that they don't pay out to any victims.)

Except for the very dangerous, it wouldn't make sense to have arbitrary imprisonment, given competition in the insurance market and ease of entry by non-profits.

As for the rich: setting up the right incentives so that they don't abuse others with (relative) impunity is a problem under any system, no matter how much it relies on jails. Even if jail is a possibility, they have far more resources with which to manipulate the justice system.

Someone extremely rich who has also revealed willingness to commit serious crimes is that much more dangerous and would have to consent to far more restrictions to buy insurance or set up a valid insurer. The cost is not just compensation paid, but in being regarded as a greater risk in direct proportion to their higher wealth.

Edited to fix some phrasing and change the excerpt I was using in the first quotation.