The problem with doing loser pays in the US is that in the US we use private civil litigation to handle things that would be dealt with by government regulators and agencies in other countries. For instance, we rely on civil litigation to enforce consumer protection and civil rights laws to a larger extent than others do. Loser pays in the US would discourage a lot of meritorious lawsuits from individuals against large companies, because there is always a significant risk of losing even if you have a good case--a jury can be a crapshoot.
As I understand the system, there are usually two mechanisms in place to offset this:
First: The loser pays costs as determined by the court , usually on a preset schedule. It's not like the winner gets to send the loser an invoice for infinity bajillions and they just have to pay up.
Second: You can apply for having the government pay if you loose. You have to file a petition explaining how (a) there's a benefit to society in having the case heard and (b) how you're not financially fit to bear the costs yourself.