That's what insurance is for, at least as far as the owner is concerned. For the city, crime isn't sued, it's prosecuted. Fines/restitution could be used to recoup money for time spent on the case. Otherwise, punishment for the person committing GTA isn't to be sued.
because they usually don't have the kind of money that's worth suing over
Because they have no money
What do you think they do with the stolen cars, just keep them for themselves and use them to commute to their day job? The fences buying the cars (or ones leading the crime rings) sure have money.
Why not jail people who steals the cars?
Seems obvious solution. Something like 10 years in prison would stop them from causing more issues for good while.