We waited so long past when we should have gotten rid of the penny that now a coin ten times as valuable is also worthless enough that we ought to get rid of it.
If we would adopt a policy of including local sales tax in advertised prices, skipping to whole dollars would be pretty painless.
The main reason to keep at least quarters is all of the various coin-op machines that are still in service.
There's a small industry that specializes in knowing what the sales tax for a particular transaction should be at the moment it goes through.
If I’m buying online with a digital transaction you can charge whatever cents are necessary.
Right now, a company can say they sell gadget X for $999, which would not be possible if they had to work out item taxes.
The other possibility is that they now have to mark X up to take into account the most pessimistic possible tax rate and advertise the marked-up rate.
Right now, there's a huge number of elected people in the US who wield real local power through these taxes and other rules that they can make.
It's a headache but we live in the computer age and we can automate administrative things like tax calculation at checkout; we should be using systems to aid decentralization and democratization instead of the opposite.
BTW, the reason for wanting to get rid of the penny isn't so much the low purchasing value, but more that they cost more to make (~4c) than their face value, so the government loses money making them. The same is true of nickels.