That really isn't the same.
Urgent care is useless if you do not have the money to pay for it when you need it, even though insurers provide monetary incentives to go there (my insurance plans generally had a copay of $50-$75 for urgent care, but $100-$150 for the ER). You can still wait hours at these places, just like at the ER. And honestly, in such cases the care is likely similar.
You also have absolutely no coverage if you don't have private insurance or are poor enough/old enough for the government-run systems.
This system is more akin to visiting a doctor that charges more than the insurance's "customary charges" and expects you to pay the difference. You like the doctor, though, so you happily pay while the insurance still pays the portion they find to be a fair price.
It is more akin to finding out the specialists in your networks have a 6 month waiting list, but one outside the network only has a 3 month waiting list. The insurance pays a lower amount and you choose to pay the rest out of pocket for a shorter waiting time. The same thing for surgeries that aren't absolute emergencies (I do hear horror stories, but I heard horror stories in the states as well).
Above all, you are unlikely to wind up with such a bill afterwards.