A. Medical care is not "accessible to all". Obamacare at its lowest tiers does not make it affordable enough for the truly poor to get most preventative procedures. All it does (which IS better than nothing) is cover emergency services better. The demand overall really hasn't gone up that much.
B. Long wait times is something of a huge exaggeration. Nevermind the fact that we've had long wait times for certain practices already, long before even Obamacare, but most other universal care countries don't actually have that problem for situations that call for rapid response. No, you're not going to just get a check-up appointment next week with your PCP. But it's a check-up appointment, you don't NEED to see your PCP next week. Meanwhile, if you're dying of cancer or something, you're not going to be waiting.
C. If anything, I would expect pay for doctors to rise under a universal plan, not lower. Currently, pricing for medical care is all over the place. Prices skyrocket not from demand, but because of complete lack of regulation (see also: pharma). Insurance companies negotiate hilariously lower pricing with hospitals, under the understanding of "you either agree to our terms or you don't get our patients".
IMO, the only people who defend the existing medical system are the ones who've never experienced free healthcare. It's such a radically different experience. Hell, I often wonder how many people recover slower or even die because of the stress of worrying about their medical bills.