> increase their demand, and to make housing overall more unaffordable?
You're not thinking systematically. Increased demand isn't the only variable. Consider also how gov't and the market respond to increased demand and need, especially if the paradigm of normative human settlement changes. Social pressure forces changes. Diffusing pressure allows gov'ts to kick the can down the road, which is what led to the suburban debacle.
> I'm not going to raise my family of six plus a dog in a high rise.
Where did I say you must live in a high rise? Urban development isn't limited to high rises. Small towns and cities exist, yes? It's a question of density and particular patterns of urban planning that enable a healthy social environment. Traditional urban planning did a far better job of that than the suburb.
And btw, what's the problem having a large family in a high rise? Living in a high rise actually reduces the maintenance costs (both in terms of time and money). Owning a suburban house comes with more overhead. In well-designed cities, there is ample green space. In a landscape dotted with cities, you are also within reach of more expansive natural landscapes that haven't been spoiled, scarred, and deformed by sprawling suburbs.
> Encouraging happy, productive families by subsidizing suburbs is good.
I assure you: the suburb is neither good for families nor productive. They are extraordinarily wasteful. Children are shackled and isolated at home, because getting anywhere requires driving. Parents are then burdened with the task of driving their children everywhere or making arrangements. You can't do or buy anything without driving. People waste countless hours commuting. And as I already wrote, it is very expensive to maintain suburban utilities. It takes a lot more energy to keep the suburban machine running. Suburbs are basically on gov't welfare funded by city tax payers.
This naturally comes off as entitled: entitled not to live in a high rise (which, as I said, is not necessarily entailed by the word "city", so rather moot) and entitled to subsidies that drain resources from cities. Why don't suburbs pay for the luxury of their own existence? Funding them is not a matter of the common good, nor is it charity. It's exploitation of others to satisfy a private fetish and fantasy, one that incidentally harms the common good.
I encourage you to visit Strong Towns[0]. There's plenty of material there that targets a popular audience that covers this subject. You might find these ideas less threatening than the urban boogeyman of your mind.
[0] https://www.strongtowns.org/