It causes noticeable dropoff in stores. I don't remember the numbers, but we did an A/B test and noticed a difference. We switched to referrer URLs for discounts instead. I wanted to try an experiment of putting a bunch of low value discount codes out there that would have been easy to find, and see how that affects dropoff, but we never did that.
To me, coupons are always seen as temporary gifts from the company to butter up my loyalty. So paying full price still feels fair.
But again, it's all about metrics. It would be great to see how different audiences respond.