At what point can you reduce the cost for developers so that affordable/low-income housing becomes profitable? If you can answer that question, then you may have solved Boston's housing problem. I'll wait.
Without subsidies and unlimited supply, building housing for low-income tenants will never be as profitable as housing for people with middle- and high-income. Period. This is true everywhere, even in markets without "Boston's housing problem". But it doesn't matter, and we don't need to reverse this in order to address our housing affordability crisis.
Low income housing doesn't need to be profitable in order for it to be more affordable. If you build enough profitable middle- and high-income housing it will take pressure off of those with low income. And revenue from middle- and upper-income housing can be used to subsidize low-income housing. This is how you address housing affordability for people on the lower side of middle income.
And as far as people with truly low income, it's important to remember that low income people really don't have a housing affordability issue. They have an everything affordability issue. When low income people can't afford medicine, we set up medicaid. When low income people can't afford food, we set up WIC and SNAP. When low income people can't afford to send their kids to school, we set up public schools. These are the ways that the necessities of low income individuals are usually addressed. We don't say "At what point will hospital stays for low income individuals who can't pay become profitable? I'll wait."
So yeah, allow developers to build as much middle- and upper-income housing as their profit motive desires. As more housing gets built there will be less competition for existing housing; this helps everyone who rents in the existing housing the same way it helps those who move to the new housing.
There is also a qualitative factor in Boston's high housing cost that is hard to analyze with traditional economic supply/demand modeling - there are only so many Beacon Hill/ South End type neighborhoods in Boston. Certain urban neighborhoods whether its Greenwich Village in NY, Park Slope in Brooklyn or North Beach in San Francisco are so scarce and not going to be easily replicated. Assuming crime etc is not out of control and the quality of life is good the wealthy or those with excess disposable income will continue to gravitate to these unique and relatively scarce neighborhoods in significant numbers to the point demand will exceed demand. I'd speculate that these neighborhoods play in the role in the desirability of nearby housing even if it does not share the same characteristics. For example the bland high rises of Charles River park benefit from their location adjacent to the allure of Beacon Hill, etc. Boston could build dense town home communities on zero lot lines but I'm not sure it would lower the cost of housing in central historic Boston neighborhoods. The reason being is that these types of neighborhoods are so unique and scarce across the country.
In the big picture, this doesn't matter. These fancy neighborhoods are such a tiny slice of overall supply. Super supply-constrained neighborhoods will always be super expensive as long as they're in high demand, and that's fine. I don't care about pricing on Beacon Hill, I care about pricing overall. And tiny areas like Beacon Hill do very little to affect overall prices.
If you look at it in the bigger picture sense of "Boston housing overall is in high demand", well then, yeah, that matters. Basic supply and demand theory: when demand is relatively high and supply is relatively low, prices go relatively high.