It’s really not that simple.
You can, for instance, buy land and build your own home. But if you do that, you’re likely going to end up paying prices that are very comparable–or much, much higher!–to the prices you would pay to get the mass-produced homes from one of a few companies that are building massive sprawl. Those companies have economies of scale working on their side; they have limited floor plans, and have more control over the cost inputs, because they can negotiate bulk pricing. If you break up the ‘cartels’, then you’re suddenly dealing with much, much more custom homebuilding.
(FWIW, I’m currently looking into custom homebuilding, so I’ve got a pretty decent idea on what some of the costs will be for even a fairly modest home where all I really want is a shell that’s stub plumbed and has a breaker box.)
The problem isn’t political will per se, but specifically steamrolling local NIMBYs. The people with the most political power and will tend to push high density housing out of more desirable areas and into less desirable areas. If you wanted to, for instance, but a 100 unit building in Ukrainian Village or Wicker Park in Chicago, you’d have a really stiff fight on your hands from local property owners who want to keep their neighborhood all brownstones. OTOH, if you want to demo a square block near Garfield Park and build there–and I wouldn’t recommend doing that–you’ll have the local alderman holding a golden shovel for the groundbreaking.