Where I'm from (Scandinavia), we have laws like that. You pay for your and the other sides legal fees.
While you rarely, if ever, see cases where losing parties have to pay millions - I personally haven't seen any like that - you can see people having to pay tens to lower hundred thousand $ in legal fees.
That can be a substantial sum for regular people, and those circumstances happen when the other party has hired in high-$$$ lawyers, and the case goes on for a while. Especially if there's multiple appeals.
So there's always the risk of that.