Cavan Wilk, reprising an old argument from Jane Jacobs, argues that a stock of old buildings is key to making an area affordable. I think this is largely a misunderstanding, though it does contain some elements of truth.
One misunderstanding is simply getting the causation backwards. If you take an area where there was a lot of demand for structures once upon a time, but currently demand is low, then you're going to find cheap rents and old buildings. Conversely, if you take an area where demand for structures has historically been low and currently demand is high, then you're going to find high rents and new buildings. But in these cases it's not the age of the structures that's driving the rents, it's the rent that's driving the age of the structures. High demand relative to the stock of structures is creating both high rents and new buildings. But if you prevented the creation of new structures, the rents would be even higher. That's why a historic neighborhood like Georgetown in D.C. can become extremely expensive, even more so than a neighborhood full of shiny new luxury condos.
The other misunderstanding is just running together age and quality. If you have expensive land, one way to make dwelling on the land cheap is to ensure that some of the structures built on the land are low quality. A low quality structure may be an old structure since old structures may, in Wilk's words, lack "the latest amenities." But for policy purposes it's important to be clear that it's the low quality rather than any of the more meritorious aesthetic features of old buildings that's driving the affordability here. If you go to Park Avenue in Manhattan, you'll find plenty of old buildings that aren't even slightly affordable. That's because they're not low-quality buildings! But if New York historic preservation law had prevented the installation of air conditioning and cable television to those buildings, then we'd be looking at a very different scenario and the stock of old buildings would become a stock of relatively affordable housing.
But that would be a fairly strange affordable housing policy. The first time a low-income senior citizen died for lack of air conditioning in the summer we'd be revisiting its wisdom. The sounder approach is to realize that if you want a lot of people to be able to afford to live in walkable, transit-accessible neighborhoods then you need to allow developers to build lots of housing units near train stations. If even when housing is plentiful some families can't afford it (which will likely be the case) then the solution is to give those families more money. But if the problem is simply that housing is too scarce, then promoting low-quality building stock is not a real solution.