The OP acknowledges it was his fault for leaving the $$ in the first place, but that doesn't invalidate his statement that one should be able to leave things in one's personal belongings (such as backpack, luggage, undies, jean pocket) without them being searched by an employee.
And as bdschobel mentions, not everything fits into an in-room safe. My laptop doesn't, and I'm not about to run down to the front desk to check it into their safe (which has a disclaimer/limit on what can be claimed btw) each time I'm in/out of the room.
The OP will have to chalk this up as $200 lesson learned, but the hotel management/security team needs to be informed as well that they have a thief amongst their employees.
Cheers.