They already do. People paying all cash saves the seller at least three months. Sometimes the bank won't close for 8 months because of reason and then denies the application forcing the seller to start from the beginning.

People do accept all cash bids for less than asking. People know this, and there are tons of places that will pay all cash for your home right now for less. If you live in a place condo or a house, you will get letters asking to buy the house all cash.