to be fair, having only 2 decimal places isn't an inherent feature of government currencies; it's simply the way banks and other institutions store amounts.
there's no reason why a pack of gum couldn't cost $0.4529839 if being paid for electronically.
In theory, yes. In practice, we are heavily dependent on tons and TONS of bank & payment infrastructures, with billions of different standards and implementations.
It's indeed the way the banks work, as you already mention, and there's no simple way around them if you want to stick with euros and dollars.
It would be virtually IMPOSSIBLE to get $ 0.000001 units actually working in practice, and would at least take many many many years of development, insane debugging / hacking / workarounds, deciphering tons of spaghetti code on crummy old systems, and disentangling a plethora of highly non-standardized finance processing programs, modules and servers. Not gonna happen.
Bitcoin, on the other hand, is very clear about this in its protocol specifications (theory) AND it's been implemented perfectly in every client (practice). So, there's one problem that Bitcoin solves.
There is no demand for sub-penny units in USD because sub-penny units will always be worth less than the cost of caring about them. They are rounding errors.
The only reason they matter in BTC is the expectation that the BTC will appreciate to the point that these small units will be of significant worth.
That said, divisibility past hundredths is not a flagship feature of bitcoin or why someone would want to use it instead of dollars. Freedom from the banking industry and government control of money is the reason why to use it.