While Amazon may have the administrative capacity for handling the filings, that doesn't address the tax revenue politics + considerations (which i didn't write much about in my earlier comment).
The issue of state tax breaks was such a big deal during their "HQ2" contest a few years ago that it actually became one of the top issues in the NYC elections that year. (to a large extent local candidate races became a referendum on how they felt about giving tax breaks to amazon in exchange for Amazon's commitments to employ a certain # of highly paid software + product people who would potentially contribute to the overall tax base. NYC people ended up electing politicians to stop the previously-negotiated pending deal with amazon, and amazon got enough blowback to say 'we give up' publicly.
The issue of state tax breaks was such a big deal during their "HQ2" contest a few years ago that it actually became one of the top issues in the NYC elections that year. (to a large extent local candidate races became a referendum on how they felt about giving tax breaks to amazon in exchange for Amazon's commitments to employ a certain # of highly paid software + product people who would potentially contribute to the overall tax base. NYC people ended up electing politicians to stop the previously-negotiated pending deal with amazon, and amazon got enough blowback to say 'we give up' publicly.