If you need stitches in the UK, that's an A&E (ER for my North American friends) sort of ordeal, and yeah, you won't be seen immediately because the system is badly managed and overwhelmed. You'll have to wait several hours (unless you're bleeding out/at risk of death, in which case you'll be seen quickly), not 43 months ffs.

Similar situation just about anywhere in the US as well. So many Americans buy into the myth that the high prices keep American healthcare fast and efficient, but in reality you're still likely to run into the same problem of waiting half a day in the emergency department waiting room, difficulties finding a primary care provider taking new patients, and months or years-long waits to see a specialist.