I discounted at launch and it took two years to undo, so here is the honest version of the risk you are describing.
What happened: fifty percent off for launch week, a good number of signups, and a cohort that never moved. Every attempt to raise them produced churn and unhappy emails, so I carried them at the old price. Meanwhile the discounted number was the one in every screenshot, every review and every conversation, so new prospects arrived expecting it and full price felt like an increase rather than the price.
The part I did not anticipate: a discount selects for the people most sensitive to price, and those are also the ones most likely to churn, most likely to ask for support, and least likely to give you useful product feedback. My best customers came later, at full price.
What I would do differently, and did the second time:
Discount the first period, not the price. First month at a low rate, then the real price, stated clearly up front. Urgency without a permanent cohort.
Or give something that is not money. Extra usage, a longer trial, early access to something, a call with me. All create the reward without touching the reference point.
Or do nothing. Launching at your price is a legitimate and underrated option.