It matters alot. Both the employee and employer are benefitting from government spending, the employee shouldnt have to foot the whole bill. That is dytopian
If corporations were able to operate in a high trust fashion and actually take responsinility for their tax burden properly, instead of trying to shirk it, then this policing wouldnt be needed, but we dont live in that world
Suppose amount of money an employer is willing to pay for an employee is $100,000. For the employer, if there is a $20,000 payroll tax, then the employer would only pay the employee $80,000 to keep the total cost at $100,000. If the employee pays the tax, then the employer will pay the employee $100,000, then the employee pays $20,000 and has $80,000 after taxes. Either way the employer pays $100,000 and the employee gets $80,000. It doesn't matter which party is paying the government $20,000*.
Now, there are other tax schemes that aren't based on how much an employee is paid, but that is a completely different matter.
And FWIW sales/vat tax is somewhat similar. It doesn't matter if the buyer or the seller pays the tax, either has the same effect on the total amount paid.
Either way, the total cost of employment is higher for the employer than the after-tax income of the employee.