Don’t you have fee when initiating a lawsuit ?

I don’t know in the USA but in France, if it’s deemed that you launched a lawsuit knowing very well it wouldn’t succeed, you are susceptible to get a 10k€ fine. Even jail in serious cases.

Yes. And you(r lawyer) can collect lawyer's fees and you can be made to pay the court fees, if you lose.

IME the American legal system is set-up to discourage litigation, though. A common tactic is to bury your opponent in the threat of heavy damages or jail-time to get them to settle for what you were originally after, which courts are perfectly happy to facilitate because it gets a potentially lengthy trial off their dockets. They'll punish (or be biased against) whichever party seems responsible for not accepting a "reasonable" settlement.

Algorithmic abuse of the system to extract payments already exists in the form of the debt collection industry.