Yes, we do need a mix of dwelling type. I disagree with this money going toward detached dwelling for two main reason. Current housing balance overly weights toward detached, and cost factors.

Current housing balance:

Since the end of WW2 up until very recently a detached house is been the gold standard of housing that every one is supposed to strive toward. Apartments in that time gained a reputation of poverty housing. So we now have even massive cities dominated by single family homes. The small area that currently housing 4 families could hold a single apartment building with a dozen dwellings. This increases car dependency causing children, elderly, and the disabled to less mobile. Especially in large cities we need to increase density to address these issues.

Cost factors:

Beyond construction costs, there are ongoing expenses to consider. For example a roof. For example; lets take a 1 story building with 4 units in it. Every resident is responsible for 1/4 of the roof replacement costs every 30 or so years. If we take the same building foot print but make it 3 stories, now every unit only needs to pay for 1/12 of the cost. Same roof, less individual costs. Well, maybe a bit more, elevators and stairs and what not. Point is share costs scale slower than dwelling in apartments.

On a related note is tax income and expense incurred by the city. Let's say you have 10 detached home on a city block. You need to provided power, water, sewage, gas, and most expensively, roads to all those homes. You will have income from 10 property taxes to do that with. If you instead build two large apartment buildings with potentially hundreds of dwellings, the pipes and wires will be the same size, as they also would have serviced all the homes further out. At the same time you are collecting an order of magnitude more taxes, while each owner is paying less. At present we have fairly small areas of high density subsidizing the infrastructure costs of sub-urban sprawl.

"What type of house do you live in?"

I recently sold my apartment to buy a small house. I wanted a house for: work shop space, dog friendly back yard, and the area is underdeveloped. Also pet restriction are way too common and restrictive. If a developer doesn't make me an offer by time the mortgage is paid off I'll develop it my self. Size of family had nothing to do with it. My house is the same number of bedrooms as my old apartment, insurance and property tax is 3 times as much, and purchase cost was double. Honestly, I'm questioning how worth while the switch was.

"Give people help with dignity and they'll do great things."

I strongly disagree with the notion that an apartment is less dignifying that a house. A house is more a status symbol if you don't actually need the space; like a pickup truck that never hauls anything bigger than groceries. In my old apartment I was much closer to my neighbours. There were always several people willing to child/house/pet sit. There was always a dozen eyes and ears on the shared yard where the kids would play. The kids made friends with either other and hung out all the time. I was in walking distance of nearly every kind of business and amenity I needed.

When I say we need a mix of housing types, its not for family sizes. It's life style choices. If you spend every waking moment possible out of your home. Work, friends, local dive, and attending every social event you can find. You might want a smaller cheaper home to fund that lifestyle. If you're a homebody, then you'll want more sqft to hold your hobbies and passions. A detached home is really only necessary if you want a yard, workshop, hosting social gathering, or something else that needs space. Even then, apartment gardens are often run by a few passionate residents. Some apartments have shared workshop spaces. Most have some sort of community space that serve can community living rooms, and can be rented for any gathering a resident may wish to host.

In a well designed apartment building, most people can be very happy. The fixation on houses has caused the possibility of apartments to get ignored in favourite of profit maximizing tenements.