Interesting watching this thread develop. I think there seems to be some consensus that in a hotel outside of Vegas this just wouldn't be appropriate. As a Brit, even one who spends a lot of time in the US, I do struggle with the tipping culture.
It seems like everything requires a tip in the US these days; valet parking (even if you've paid for it), housekeeping, bell service, servers, concierge - all on top of a ridiculous resort fee and service charge. I've never heard a convincing argument for resort fees. They're a complete rip-off and shouldn't exist. Why not just build it into the price of the room and pay everyone properly? It makes it so much more pleasant for the guest.
The argument that good service is encouraged by tipping is a misnomer. If staff are paid well, feel valued and enjoy their work then they will give good service.