Not reporting any accident to your insurance company prevents you from being protected from liability and you risk discovering down the line that the repair wasn't done properly.
If the accident wasn't your fault then you won't be charged higher premiums. At least in the states I've been insured in.
I would definitely want the hotel to provide a police report or a letter or email stating the damaged was caused by a valet.
Surely they didn't refuse to waive your parking fee when asked? I'd hope they just didn't think to ask the front desk to remove it?
I'd ask for a rental car reimbursement during the repairs if your insurance doesn't cover that.