Criticism just from wikipedia page:
Companies complain that these loyalty programs discount goods to people that are buying their goods anyway, and that the expense of doing these programs rarely show a good return on the investment. Other critics see the lower prices and rewards as bribes to manipulate customer loyalty and purchasing decisions, or in the case of infrequent-spenders, a means of subsidizing frequent spenders.
On the other hand, a 2015 study claimed that most supermarket loyalty cards in the USA do not offer any real value to their customers.
Commercial use of the personal data collected as part of the programmes has the potential for abuse. It is highly likely that consumer purchases are tracked and used for marketing research to increase the efficiency of marketing and advertising; in fact, this can be one of the purposes of the loyalty card. To some, participating in a loyalty program (even with a fake or anonymous card) funds activities that violate privacy.
In short, manipulative behavior that serves no real value other than increasing revenue for shady marketing companies.