I'd say screw it, get rid of nickles and dimes as well. Quarters can stay, for now.
It's a complete waste of money and time continuing to mint such low-value currency. It can't be used for just about anything.
Unfortunately, I do see the problem with part of this. For a handful of items where it does matter, it will force people to use cards more if they want to avoid rounding. And the card providers already have a choke-hold on retailers, and the whole thing is basically a scheme that funnels money from the poor to the wealthy via interest and fees on the consumer, interchange fees, and rewards programs.
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