I suspect a major factor is that the fee, when paid by the tenant, acts as a filter to shut out less desirable (i.e. poor) tenants and those who might not stay long. This is possible because demand vastly outstrips supply.
At least it's like that here in Germany - the broker fees for good apartments are almost always paid by tenants. Any apartment where this is not the case has probably major downsides. In other cities, where the supply/demand situation is different, broker fees are paid by the owners and the broker's added value is marketing (i.e. finding good tenants at all)
broker/makler fees in Berlin are usually paid by the owner as far as I have found. this may change now that demand is so much higher than supply. it certainly wasn't like this 5 years ago.
Yes, Berlin still has (or at least recently had) an oversupply of living space. Look at Hamburg or Munich, and you'll see that nearly every listed apartment has the broker's fee of 2.38 monthly rents (legal maximum) payable by the tenant.
At least it's like that here in Germany - the broker fees for good apartments are almost always paid by tenants. Any apartment where this is not the case has probably major downsides. In other cities, where the supply/demand situation is different, broker fees are paid by the owners and the broker's added value is marketing (i.e. finding good tenants at all)