"therefore landlords take that x% and call it cost of living" is even less convincing
Do you dispute that?
The mechanisms are the same, though. Amazon putting HQ2 in a city causes rent to go up (higher productivity).
A coal mine developing a new, more efficient train to move coal around will also cause rent to go up (higher productivity).
2. That's a really naive sense of economic productivity. Here is a thought experiment.
A) Let's shut down all of Amazon HQ1.
B) Let's shut down the dams that provide 86% of Seattle greater area's electricity.
Which one of these entities is ACTUALLY responsible for that "productivity" then? And I bet you rents in Seattle without electricity would drop far greater proportionally than they do out by the dams. Rent follows incomes, not productivity.