but that number should be based on calculations of how much money it will take me to live the rest of my life/recoup monetary damages.

Well, most of the time the plaintiffs are mostly asking for compensatory damages for things like medical costs and future lost earnings. But seeking punitive damages for serious fuck ups or gross negligence is also sometimes part of a lawsuit and is the cause of those really big number lawsuits that your talking about, so sort of think of that aspect like a fine in order to deter others from negligent behavior. You usually don't see those multi-million dollar suits that are for honest mistakes, they're usually for gross negligence, repeat offenders, malicious intent, etc. and that fear of lawsuits has been found to make medical practices and businesses in general more efficient and careful, so you could argue that it works. iirc the supreme court found that anything higher than 5:1 ratio of punitive to compensatory damages is likely unconstitutional so while there isn't an official cap on punitive damages in most states ( I think?) there is a bit of a ceiling on what's considered acceptable.

And of course, it's also extremely hard to put a price on suffering and whatnot. There are plenty of cases where an absurd amount of damages are awarded in the US but it's mostly of a myth. The occasional lawsuit seeking an absurdly high amount will occasionally happen and the media loves that stuff. The headlines of a lot of those cases will sell papers due to their apparent absurdity, but once you look into it a lot of the lawsuits aren't that frivolous and there's usually an at least understandable reason they're seeking such high punitive damages.