I think you are mistaken here.
In tipping countries waiters basically beg you to leave as soon as you've eaten. They are always around you to upsell something (bigger tip) or to passive aggressively bring you your check. Eating out for only an hour is common.
In non-tipping countries however, the waiter simply leaves you alone to eat in peace. They don't ask you "Do you need anything else" every 5 minutes. People on average stay out more because of this.
Which is why you feel ignored. Different cultures.
I grew up in a non-tipping country, this isn't a culture issue when some waiters are clearly hard to find in the restaurant, good waiters will leave you alone, but when you need them they will be here, or at least know when they need to take a look from far away and see if water/bread seems lacking.
This is annoying to just be frustrated when you planned to have a good night, and know that other people are going to be frustrated by that bad waiter too.
If I am unlucky and have to get a terrible waiter, I appreciate the fact that he/she is going to provide a minimum service because of the tip.
Fortunately, for non-tipping countries, reviews like Yelp/Foursquare/... kind of help the market I think, you can see what the reviews says about the service.
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.
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.
This is not true, in my experience. I have dined extensively in the USA and in many other countries and have not noticed any difference in the level of service provided.
With tips you get some clear advantages over non tipping. The waiters have a huge incentive to give you a pleasant meal experience. This is very annoying to go to a restaurant and it appears to be more complicated for you to get water than it is when you're eating at home. This is what you often experience in no-tipping-countries restaurants. The tip is like an implicit contract with the waiter: Deliver me a good service, I will pay the price.
The cons: What about the kitchen staff, the host/hostess, do they get part of the tip? What happen when the food is terrible but the service awesome, or vice versa. But most important, as acjohnson55 mentions : but it also exposes them to discrimination. Sadly discrimination is real and tipping here doesn't help.