I am not sure to understand, from a company point of view, why a company should implement a cryptocurrency instead of the traditional loyalty program. And the same, from a customer point of view. Why a customer would prefer a cryptocurrency instead of the loyalty program.

Are you talking about a cryptocurrency that could be listed on an exchange? Or just a token usable on the site only. Because in case it's about a crypto I see a problem in. Let"s says the token triple or more within months, the company will so start to see reduced profits and so losing money.