It hasn't though and no it's not how it should be. Any kind of payment comes with a fee. Yes even counting cash at a bank isn't free. Paying a security firm to come pick up cash regularly isn't free.
And the hotel has accounted for this in their price. Apparently they find it 1-2% cheaper. It's only unfair if they only accept credit cards, and still add a hidden fee.
They don't. You're assuming a lot of things. Extremely few people pay cash at a hotel (as even deposit would have to be in cash and held in place and refunded in person). Vast majority pay with card.
They're doing this because they can get away with it. Purely and simple. Large part of this 2% is extra profit.