Who would travel with 90,000 in cash? Sounds like a scam to me.

And in every single hotel I've ever stayed in, the hotel management have had a key to my room. How else will they clean my room if they didn't?

The policy is the same in every hotel in the world - the hotel isn't responsible for lost or stolen items. You would be a fool to leave 90,000 in cash in your hotel room and then be surprised if it got stolen.