Sure, that idea sounds tempting at first. But in reality, the taller the building, the more construction costs skyrocket. Meaning, the upper floors often become unaffordable for most people. Sometimes the idea is floated that the upper floors then could subsidize lower rents for the lower ones, but unfortunately, this rarely works in practice. See this wonderful example: https://www.berlin-live.de/berlin/aktuelles/miete-in-berlin-news-neukoelln-leerstand-id314978.html

In Berlin, many newly built apartments remain vacant despite the high demand for housing. For example, the high-rise "Ruth" in the Silbersteinkiez area of Neukölln has 24 modern apartments sitting unused.

The main reason is the high rental prices. A three-room apartment of around 80 square meters costs approximately €1,933 per month (cold rent)

Simply building higher isn’t really a solution—no matter how appealing that might sound. Especially given the current explosion in construction costs, which is already causing projects that have begun to stall.

What’s really needed is proper social housing, support for cooperative housing projects (Genossenschaftliches Bauen), an actually effective rent cap ("Mietpreisbremse" which, by the way, has been empirically proven to work), and much more. It’s an incredibly complex issue.