Rounding up and down is exactly what the Army/Air Force Exchange stores did overseas when I was stationed in Europe. I didn't use pennies for 16 years over there and can get on board with this based on my experience. Though, I'm not sure about any 2nd and 3rd order effects if implemented on a nationwide scale.
Yeah, the 2nd and 3rd order effects are my concern. Don't get me wrong: I very much doubt this would have any significant effect under any circumstance, either way. It's just bad policy to create scarcity instead of addressing the real issue.
An example on a much larger and consequential scale: after the financial crisis of 2008, there were many people who wanted to sue the credit ratings agencies (CRAs) into oblivion. IIRC, the CRAs have some legal protections that are sort of bullshit (including, preposterously in my mind, free speech), so they wanted to get rid of those. The problem was that the CRAs are deeply embedded in American law. States have laws that prevent fiduciaries from investing money in any security not rated AAA (or the equivalent) by a CRA, for instance. If we sued the CRAs out of existence (or legislated them out of existence), then what? The problem would arguably get worse.
Fortunately, these were serious people having the discussion, and they soon realized that you can't get rid of the CRAs unless you first expunge legal requirements related to them. And so began a move to decouple our fiduciary laws from CRAs. I don't know just how successful that was.
The CRAs are abominations, and it still boggles the mind that we have a system in which debtors pay for their own debt ratings. But you can't get rid of them without surgery. And that would be my concern about not minting pennies while they are still legal tender. Again, a small concern. Even if this plan went sideways in the maximum possible way, it would be a rounding error on the federal budget and the economy. Still, on principle, the best way to stop printing pennies is to eliminate them from legal tender.