I actually hope this is a city where housing affordability is made more sustainable up front. Something to avoid the way New York and San Francisco have evolved into landlords and rent seekers drowning the wealth generation of incumbents
If Amazon decides to build housing and includes below market rate housing for low income people this could work, but given the focus on subsidies and tax breaks in the RFP, I highly doubt this will happen. My guess is that this will only increase strain on whichever housing market receives the HQ.
Manhattan has been expensive for a very long time in spite of growing housing significantly.
The challenge is that they can go to places where housing is cheap and there's a lot of capacity. Detroit, Las Vegas... But they'd probably still have trouble attracting a lot of tech workers to those areas. [ADDED: Although Michigan is better than people in the Web tech bubble think in this regard.]