I think payroll taxes are different from other corporate taxes in that they are a direct tax on wages, and thus directly increase the business's cost of labor. Businesses don't really care what part of their labor costs are taxed on their end, what part is taxed on the other end, what part goes to various benefits, etc. They just care that it costs them $X for a given employee.

It is quite possible that reducing the employer side of FICA wouldn't translate into a 1-to-1 higher paycheck, or even any increase at all. But the same is true of the employee's side, or of regular income tax, or any other tax.