Suing for damages here isn't profitable enough for attorneys, because "damages" with free healthcare means "missed a week of work", instead of "got a $200k bill".

It does happen, but it's way less lucrative. Tends to be limited to actual damages rather than punitive damages. There have been some scam-ish sub-industries (fake whiplash claims, suing councils for tripping over cracks in the pavement). It's very rare to see advertising for lawyers.

Insurance and worker rights probably takes care of that here. What is it that personal injury lawyers usually do?

FWIW it took me multiple US television shows to figure out what "ambulance chasers" are and why they exist.

lawyers or law firms are very limited in how they are allowed to promote themselves.

Most non-US countries only award money for actual damages, not punitive charges.

It's also assumed that people have at least a little common sense and that your average adult knows more than a toddler.

mostly handled by insurance. Payouts are also a lot less, and typically standardized.

Personal injury cases exist everywhere, but most countries impose very strict restrictions on legal advertising, which greatly reduce the phenomenon of the "personal injury guy" who plasters his face everywhere with text about how much money he'll get you. In the US, most such restrictions were prohibited by the Supreme Court in the 80s.

WAY less than in the US

But no you don't have ambulance chasers or personal injury lawyers trying to get millions out of someone who had a car crash and now their neck feels funny

Not on dirty great billboards, no. Not yet.