That's probably a good problem to have! Nonetheless, customers are still buying from the same store, so, it's a win-win. Breaking customer trust is probably the only thing that's bad here.
Yeah, it's a tradeoff for sure. I would say discounts that don't apply to everyone are a less organized way of a/b testing price. So a brand that does discounts all the time on certain cohorts of their users is going to have an easier time swapping over to using [name-redacted] vs. a brand that has 1 price, no discounts ever, never have changed their price.