You are speaking of the Employer portion of social security tax (aka Self Employment Tax).
All the happens when switching from contractor to employee is the salary goes down, so the final cost to the employer is identical. (And the income of the employee is also identical.)
A contractor vs employee is about flexibility on hours. An employee expects a certain number of hours per year - all the benefits are based on that.
A contractor has no such expectation, so they have no benefits (because otherwise you would have to scale the benefits up and down constantly based on actual hours worked).