And to your first point, the high cost of housing doesn't seem to be impacting the desirability of Boston at all. This place is growing. Fast.
Does lack of affordable housing decrease the desirability of New York? Not in the least. The high cost of living prices out almost everyone, and yet there are more and more people cramming into New York year after year. There are plenty of people who will bear the high price, even if you personally aren't one of them. Same goes for Boston.
It's simple supply and demand. If prices go higher, that means supply is rising more slowly than demand. For prices to be lower, the supply of housing would have to rise more quickly, expanding the amount of housing available, therefore allowing more people to migrate. There are people who are priced out of Boston. The constraint on growth in a region is almost always related to the supply of housing, not the number of people willing (meaning there is any price for which they would choose Boston over another city)to move there.