So the bill does address this concern.
The bill addresses that by requiring each state to provide software free of charge to retailers that does that for the entire state, and by providing explicit uniform rules for sourcing (well, technically, there are two sets of sourcing rules -- one in the bill for states that are not part of the "Streamlined Sales and Use Tax Agreement", and one in that agreement that the bill adopts by reference for states that are a member of the agreement.)
You provide the sourcing information (applying the rules in the bill for sourcing), the state software provides the tax rate. The state software is the only part that has to care about identifying substate jurisdictions and applying their rules.
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.
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.
ADD: "Since integrating 50 different software packages into every online store, filing 50 different sales tax returns, cutting 50 checks, and getting audited by 50 states is not an appealing idea to most small businesses, they’re almost guaranteed to pay a certified software provider to handle it."
I'm a little confused. As I understand it, there are over 9,000 various jurisdictions -- down to the zip code+4 level that implement various forms of sales taxes. You can be on one end of a street and pay a completely different tax than you would on the other.