Yes, of course, they can. But what you're suggesting is they'll do that absent tax breaks, which suggests cost of a location is a primary factor in HQ openings,

Yes, of course, they can. But what you're suggesting is they'll do that absent tax breaks, which suggests cost of a location is a primary factor in HQ openings, which seems obviously wrong given the choice of NY/DC. And it's not like Amazon is alone here. Despite NY/California being, uh, not known for tax friendliness, most major companies in fields concentrated in those areas still put their headquarters there.