The best way I can describe our healthcare is that it's freakishly complicated, so complicated that pretty much every argument made by any side at any given time is both correct and incorrect.
For your example about single payer, with that scheme costs will likely be much lower but on the flip side, we also would not get immediate access to care (that is you can't attend a doctors appt within 72 hrs of scheduling) and we also would not get access to the latest and greatest drugs and therapies because those are always expensive and SP schemes typically do not cover that.
Now with that said is single payer good or bad? Well it all depends on who you ask. If you ask a 20 something that just visits the doctor once a year for a checkup and maybe calls into urgent care once every few years when the get the flu or food poisoning, that person will be all over the moon about a single payer system.
Now contrast that with someone in their 50's or 60's that has pre-existing conditions, sometimes chronic conditions, and needs constant care and access to the latest drugs. Well for that person single payer is dogshit and won't cover half their needs.
And that is the essence of the problem, two sides with vastly different needs from the healthcare system and a government that has to make one decision that will somehow satisfy both parties, even though that could really never happen. You're either going to pick the 20 year old and screw over grandma or you're gonna pick the grandma and screw the 20 year old.