Look its a condition of employment, just like FedEx requires you to wear black shoes to work there, if you don't you get sent home(or fired if you continue to not comply) it's something you agree to as a condition of employment.
Much the same way you agree that you/possessions/vehicle may be searched, as a condition of employment.
Believe me I want to agree with you, its a crappy deal but the more I read the more I learn.
Feel free to cite sources why you believe otherwise.
As for the 4th... you may want to read a bit more on it. But conditional employment would trump the 4th even if it applied
"Public employees work for the government, so any action by a public employer is by definition a "state action" and subject to the Bill of Rights. For this reason, employees of any level of government have the constitutional right to be protected from unreasonable search and seizure as guaranteed by the Fourth Amendment to the U.S Constitution. However, the Constitution only applies to state action and not to the actions of private employers. Public-sector employees have greater protections against workplace searches from their employers than private-sector employees do."
Private-Sector Vs. Public-Sector Workplace Searches
"The law regarding employee searches involves a careful balancing of the employer’s right to manage his or her business and the privacy rights of employees. For example, the Fourth Amendment to the United States Constitution provides protection for all persons against unreasonable search and seizure of their persons, homes, and personal property, and this doctrine applies when the employer is the government. However, most private employers are exempt from this doctrine"
The Limits to an Employer’s Search