that is the fear of well insured prior to ACA -all countries with socialized health care also have waiting lists.
My country was like america before but then they made getting the basic insurance package compulsory for everybody (it was never provided through employers btw, it's a personal thing you buy), with of course welfare to make sure people who cannot afford it (but aren't poor enough to be on the dole) have it too.
I think they also banned refusing the basic coverage to anyone who asks for it or something, there's LOTS of regulation in the sector and weird and complicated stuff.
There are e.g. compensation mechanisms to prevent companies from gaining an advantage over the others by hunting for healthy people.
There are no waiting lists and you choose your doctor, unlike in the UK.
So if waiting lists happen, it's not because of compulsory healthcare insurance, but because of other reasons.
I have yet to see the perfect healthcare system, the one in my country is good but costs a lot of money and there's lot of arguing about what to do about it. The socialized system leaves you with no free choice and long waiting lists. The american system is not solidal enough and does not support preventive care since people who aren't insured will probably skip out on it.