A city should be worth it to live in and provide enjoyment for the citizens, not be a glorified chicken coop for people.
Otoh sprawl development leads to dead neighborhoods, car dependence and long commutes. It also uses space that could be left to nature instead.
There is a middle way between US-level sprawl and Japan-style chicken coops - and I definitely hope we don't go the Japan route.
Here in Prague we have quite a few brownfields that could be home to at least 50 thousand people (Rohanský ostrov, Bubny, Kolbenova), but the development is extremely slow.
Well having some undeveloped space is actually quite nice to enjoy in a city. We don't have to live packed narrowly on top of one another.
But more specifically, brownfields (previously-industrial spaces) are usually highly polluted. Some are full of heavy metals and chemicals that you really don't want to displace into the air by digging into the soil... Some people are doing it, but it either costs billions of euros in depollution, or greatly affects the health of nearby population, and often both.
It required several years of sanation works to clean up, but now it is built over and serves the needs of the population. [0]
I believe that this is a reasonable use of public money, even though private developers profit from it. Or possibly finance it through a Public-Private Partnership project.
The alternative is to let poisoned land within borders of a big city stay poisoned forever. Which does not sound either people- or environment-friendly.
[0] https://www.ostrava.cz/en/podnikatel-investor/real-estate/br...
The problem is: Berlin can't. There is not much free space for new construction in Berlin proper, with the exception of "Nachverdichtung" such as you propose with apartments over parking lots - and these have the downside that they are horribly expensive, simply because it costs potential developers a lot of money to acquire the land!
The solution would be to build out internet connectivity and public transport in the suburbs in Brandenburg so that employers don't all concentrate in Berlin.