* For short-term rentals (vacation homes) one needs to have a permit and pay taxes.
* Subletting your apartment without permission from the landlord is illegal, making a profit and not declaring it is tax fraud (and most don't declare them because then they'd also have to have a permit and pay tourist tax).
* The landlord has to grant permission for sublets (also whole apartments) if the tenant is temporarily moving out of town but wants to keep the apartment, but also here: no profit allowed. EDIT: The landlord has a right to review every single intermediate tenant - so he can refuse them (this basically rules out the AirBnB model in this scenario).
What really annoys people is that in the best locations there are lots of people who ignore the existing laws and the rest of society has to pay for that: by not finding an affordable space to live, by having to endure a new set of drunk neighbors every weekend who either party in the apartment or come home drunk and very noisy at 4am and who, understandably, don't participate in the house community (and yes, people tend to know their neighbors and even talk to them!).
But before adopting new laws it would have been much simpler to simply enforce the existing laws. Get all these folks who offer apartments on AirBnB 365 days a year and check whether they have all permits and taxes. Let them pay fines. Put them on a list of people whose tax-statements and books are checked annually (they do that with everybody else who commits tax fraud or just annoys the tax clerks).
Calling German laws too rigid is everyone's right, but it is also the right of German people to value diversity in their cities enough to protect it by those rigid laws.
However leftists love feeding the government even if it is a net loss for economic prosperity. They want to tax everything without understanding that taxes reduce economic activity.You certainly need a minimum level of taxation, but it's a religion with many people. Next time you rent a car, have a look at the various taxes. Then calculate how many taxes the car company is paying for that euro of revenue. The same transaction is ultimately taxed each time to money touches someone.
As far as subletting, that should be handled between the landlord and the tenant: that's a private contract and the government ought not have any say.
If there's a problem with 'drunken neighbors,' then that also should be handled contractually between the co-proprietors of a particular building.
Government intervention isn't necessary for any of this.
I remember reading an article about Barcelona and how it was actually losing money due to low-budget tourists: the city has to maintain/clean infrastructure for them, but they don't bring much income. Not sure how they tax their bars, but these people would just get wasted and puke in their parks, and the city has to clean up after them.
The correct solution is to fine bad behaviors (littering, public nuisance, overserving drunks, etc.) and instituting fees for operating businesses that directly contribute to the problem (for example bars, liquor stores).