It doesn't cost anyone anything. They can just raise prices 3 cents or whatever.
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.
Switching to round number prices would cost retailers a whole lot more.
https://www.sciencedirect.com/science/article/pii/S002243599...
https://www.researchgate.net/publication/23547242_Penny_Wise...
https://www.sciencedirect.com/science/article/pii/S002243590...
Again: Canada actually did this many years ago. The effect you predict did not appear.