Sales taxes in the US are truly and insanely decentralized.
The US has thousands of independent sales tax authorities with their own laws and regulations about how sales tax must be computed and displayed. These jurisdictions overlap, the sales tax you pay may be the aggregate of multiple different sales tax authorities between which there is no coordination.
Rounding to the nearest 5c or whatever creates a situation where in many locales it would be impossible to comply with sales tax and pricing laws because different tax authorities requiring mutually exclusive ways of making this change.
This creates an obvious need to change the law. This is not trivial because they are often written into statute or constrained by constitutional processes. It requires thousands of jurisdictions to all change their laws at the same time in the same way, which is effectively impossible. Even if it weren't the process would require several years. In many locales it requires a democratic vote -- what if the voters vote against it? Courts aren't going to let the government ignore these requirements because it would be inconvenient.
It really is a "herding cats" problem. There are many other things in the US that effectively can't be changed because there is no central authority to overcome coordination problems by fiat. Even at the level of all 50 States, resolving these kinds of coordination problems typically takes several decades.