Also good for people who want to move to Berlin as mietendeckel made it much more difficult to get an apartment. Also good for people renting through the gray market of sublets as it makes it easier for them to get a real contract.
The issue with an approach like this is that it's merely fighting the symptoms of the underlying problem. The underlying problem is that you have more demand than supply and something is preventing the market from rectifying this problem. Capping rents can only make the underlying problem worse, because there is now less incentive to create new housing.
Now, of course, you might say the thing that is preventing the market from rectifying the situation is that there simply isn't enough space. And that is partially true, there are real physical limits here. But it's not like Berlin is a super high density city, so I find it hard to believe that we're anywhere close to reaching those limits.