You really should know more about the law before blurting something out without understanding.
Employers can do all kinds of things that "society in general" wouldn't allow. Employment is not a right, it is a privilege, and employers can write up a contract pretty much detailing what their employees can do and cannot due while on the job and even in their personal life if it affects the viability of the company.
When I stated "unlimited random drug testing" it was more of an example of how to clean up the league. Of course a team wouldn't do that, without suspicion. However, if there is suspicious behavior, then the team should be allowed to test a player more often.
Finances are at stake. I'm not the only one considering downsizing my season tickets next season, or chucking them altogether. I've already made my concerns known to my STH rep. I am not the only one. The owner gets enough of these negative inquiries and he is going to want to do something about it. Spending a small fortune on season tickets, then parking, then driving great distances just to see mediocre play isn't going to cut it for me, or most people, for that matter. The teams are going to get the message and the trickle-down is going to be felt in the owners' pocketbooks.
When I worked for the government, I was subject to unlimited random drug testing. As a frontline manager, many of my employees were tested. No one liked it, but we all understood it was a condition of our continuing employment.
So, since our own federal government employed unlimited random drug testing, my guess is that you are wrong. It is not "unconstitutional."