Germany has only "soft" rent controls that limit YOY increases in rent and (selectively) increases in rents when changing tenants.
German economic orthodoxy relies very much on the need to build housing in order to deal with housing shortages and with rising rents due to housing shortages. The "soft" rent controls simply buy time to get housing projects underway. Without new housing being built, rents would still reach market levels, it would just take a bit longer.
Berlin's current problem is excessive urbanization driven by migration (1) from the neighbouring comparatively poor East German states and (2) of foreigners who speak only English and hence prefer a city that has already evolved to accommodate English speakers. Various and sundry NIMBY problems where locals oppose new housing projects also don't help.
No. Berlin problems mostly stem from the city government colluding with investor scum to build luxury apartments instead of actually affordable ones plus doing their very best to e.g. kick squats out (which help keeping down rents for all neighbors). Berlin government could easily break the necks of the investors and protect the population instead, but especially the SPD has chosen not to do so - and sell off priorly city-owned prime real estate to investors.
The investors now do "Luxussanierungen" (basically, thermoclad the houses and fix the more egregious stuff like bad wiring / plumbing that the city government had neglected over decades) and price out all the lower-and-middle-income people.
It's unlikely that there's any such thing as an actually affordable apartment in a major world city, unless we've moved the method of allocation to something like lottery or waiting list, in which case it's only affordable to a lucky few.
I would encourage anyone who thinks that luxury apartments are for the rich while single family houses are normal to consider the relative luxury of life in the actual structures (not location). You'll find that, as structures, luxury apartments are much less luxurious than lower-density uses of the same land.
The only tax that a squatter does not pay in contrast to an owner or renter (indirect there) is "ground tax", which is a negligible amount anyway.
And the only interest which the "owners", mostly in form of offshore companies, have is to make huge amounts of money at the cost of the city, so I don't have a single tear left for them.
Compared to uncapped rent that doesn't have any?
One is that they generally have multiple units, whereas renters generally have only one. So the end of a lease is a bigger deal to the renter than the landlord. Another is that the costs (in time and money) of a tenant move are much higher for the renter than the landlord.
This means that a greedy landlord can jack the rent well above market price because renters are eager to avoid the expense and disruption of moving.
if the renter is able to accept the "jacked up" price, then by definition that's the market price (for that property). The renter needs to move if they don't like the price. The landlord also don't like vacant properties, and is perhaps eager to not "jack up" the price if they find that the tenant moves as soon as they do!
Maybe that rent cap is why landlords prefer Airbnb. Rent caps are never a good idea, they have so many unforseen consequences.