No. The employer should be required to pay market rate, plus whatever they bid on the slot. Now, you could convince me that the additional fee is evenly split between the employee and the employer.

Any excess money the employee has is either spent in driving up the local rental market, enriching landlords, or sent back to their home country. Minimizing rental competition is in the best interest of US citizens. Minimizing exporting money is in the best interest of the US government.