There are several US states where, by law, retailers are not allowed to give preferential treatment to credit card paying customers over cash paying ones. Which means, in those states, retailers will be required to always round transactions to the cash paying customer's benefit, where in other states the retailer is allowed to round to the nearest 5 cents. This is going to cost large retailers millions.
Interestingly many of them had already put the work into updating the cash register software to allow for this due to the penny shortages during covid.
Let those large retailers put pressure on their suppliers. Prices haven't exactly been stable recently. I really don't think it matters, but if it did (as you claim) then surely some downward pressure is a good thing.
Unfortunately I think this is much easier said than done. No single store is going to want to make this change, because it'll make their prices look higher than the competitors'. It'd require legislation, (and even that'd likely be state-by-state legislation).
It also means a company wouldn't be able to advertise a single price for a product nationwide, since sales tax rates vary by state (and many times even within a state).
Also worth noting that Canada also doesn't include sales taxes.
Interestingly many of them had already put the work into updating the cash register software to allow for this due to the penny shortages during covid.