The credit card is required to hold your reservattion (because the cancellation policy says you'll be charged for 1 night if you don't cancel by the cancellation deadline, they have to have method of payment to hold your room past the cancellation deadline).

Paying by cash at checkout is one thing, but once again, they need a deposit of some sort until you check out. That may be more than rate, at some hotels way more than rate. On a credit card, this is all transparent. On a debit card, not necessarily so. With cash, very obvious (if they ask you for way more cash at check-in that the room rate).

You thus can only in certain situations (I'm not sure specifically about WyndhamRewards) book a room without giving a card if you're sure that you'll arrive before the cancellation deadline. (Which kinda seems to imply the hotel has to have a cancellation deadline on the afternoon of arrival for this to work!)

If you show up too late without your reservation being held by a credit card, you may still get a room (if they're not sold out), but your reservation may be cancelled, you may have to start from scratch and get a different rate as a result.

This is standard policy at hotels of all types in all programs. I'm not clear on what you expect to different at WyndhamRewards (and yet chainwide at WyndhamRewards)??? I find that cancellation policies and hold policies are more up to the invidual hotel than the hotel rewards program!