Taxes paid by your employer are indeed paid by you. If your salary is X and the company is paying Y worth of payroll tax, then they're really paying X+Y for your services, which would all be salary going to you if not for the payroll tax.
Yes, likely not exactly the same (a bit more kept by employers in overcrowded job markets, a bit less in others), but it would essentially support the interpretation that most of that is really a tax that goes out of employee "budget", or their total comp.
Yes, it probably would depend on positions and available talent, but overall and over a longer period, if applied universally to a market (say state like CA), it will be reasonable to expect salary increases (but not increase of how much is that worth because of increasing purchasing power, and increase in prices due to higher willingness to pay).
That part is not necessarily (or even probably) true, if payroll tax didn't exist the company might not pay all of that to you unless they had to.
But that's a nitpick... overall, it is true that the fully burdened cost of having that employee is X+Y, so that's the number the company needs to consider when deciding whether they can afford to hire (or keep) this person or not.