That might be a false correlation indeed, however I disagree when you say:
"there's very little to think that level of service in restaurants in the US is related to the expectation of the tip"
waiters with good work ethics will offer a great service no matter if there is a tip involved in the end or not. Those with poor work ethics however would care less about providing a good service. I didn't mean to sound insulting to waiters, a lot of them do a great job, but I think that for some waiters the financial lure is important.
More generally, if a country seems to have poor restaurant service overall, that's a cultural thing. Introducing tipping would be unlikely to change it. To think otherwise is to think that waiters are only doing their job on the hope that they get a consideration, and that without that financial lure, they'd become lazy do-nothings. And that's both highly insulting and also illogical, because there's nothing unique about the job of being a waiter that would cause people to be lazy who would otherwise perform their job adequately in every other industry.