Every example of universal healthcare I’ve seen so far pays for it with huge payroll and income taxes. Payroll taxes have a direct and demonstrable effect on wages and hiring, and income taxes would just wipe out the benefit.
The problem with your idea is that it doesn’t actually do anything to contain healthcare insurance costs. Those costs have risen dramatically faster under the ACA than before, and they were already going up quickly.
I’m not opposed to universal healthcare at all, but you can’t just hand-wave and make it ‘free’, and with those costs I don’t think you’ll see the benefits to wages you’re looking for.