Contrary to popular belief, the US isn't actually unusually litigious. European countries are just as litigious and Germany, Sweden and Austria all have higher numbers.

The reason we have more "nonsense" lawsuits is because we have a culture that says caveat emptor is a sound defense and negligence on one parties side is equally the fault of the injured party.
"Why didn't you look at your food before biting the metal fillings? It's your responsibility to make sure what you eat is safe" and "you walked on my icy sidewalk, you slipped, and now you want me to pay for your ambulance? I should have put down salt, but you should have known better than to walk there" are both reasonable statements to a lot of Americans. Hell, we have special derogatory terms for lawyers that work with individuals who have been non-criminally injured by someone else.

On paper, paying the other parties legal fees if you lose sounds good, but what it does it keep individuals who can't afford to pay legal someone else's fees to withold valid legal complaints. In an ideal world they would proceed because they were right, but we live in a world where sometimes the person in the right looses, or they reasonably thought they were and were wrong. Due diligence or actual correctness is no assurance of justice, so a lawsuit is a gamble and a more expensive one if you also have to pay the other parties costs, and if they're a business which has lawyers on staff they might not even view a crippling legal cost as an increased expense.
On the other side that business just tells their lawyer to file the paperwork, they're already paying for the legal consult so they're advised going in if it's a good idea, and if they lose they're out a few weeks of lawyer salary.

Lawsuits are a mark of people using societies tools to resolve disputes. There being more in places with higher trust in social institutions makes sense. People are willing to use the system and they trust it'll deliver justice.
The US is up there because people need to use lawsuits to make up for our lack in social safety nets, and our preposterous number of businesses are constantly using them to settle disputes.

We should eliminate the court fees entirely and provide the trial lawyer equivalent of a public defender.
A bolt in your oatmeal is a good reason to sue, and if you can't afford a lawyer to help you pay to get your tooth put back in it doesn't seem unreasonable for society to give you access to someone to help you find a path to remunerations.