The bill doesn't address what goods are taxable; those are set by states. The bill simply sets the conditions on which states can extend the sales and use taxes they collect on goods sold by vendors within the state to goods sold into the state by remote sellers.
But you have an excellent point. The software provider feature could be a life-saver.
Of course, many times these things look very different in bill form than when deployed. This sounds very similar to a "magic cloud" that exists in many architecture diagrams :)
ADD: And if you're looking at software providers, I'd be interested in running the numbers to see how their business model would work. They'd have to take payment. They'd have to be bonded. They'd have to collect from the states, provide a categorization system, keep files updated, file paperwork along with monies. Would they have to work internationally? Be categorized as a money Exchanger by treasury department? It doesn't sound cheap. But it certainly sounds like something Amazon would be happy to provide as an API.
Regarding your other points, the bill requires all tax collections to go through a single entity for each taxing state/territory. You don't file taxes with every jurisdiction.