The problem is enforcement. As it is this law is all about tractability of enforcement, it doesn't change what apartments are or are not allowed to be let/sublet but rather adds a provision that makes it illegal to advertise an illegal unit. This is because the existing law is very difficult to enforce and AirBnB moguls are blatantly flaunting it. This is the same problem with those that suggest that we don't need state laws because condos and co-ops can just enforce their contractual rules. (Also, that argument neglects rental buildings.)
Relaxing the law in the manner you suggest would make it even more difficult to enforce than the law as it stood prior to this addition.
Just like governments demand companies hand over financial information they could demand that AirBnb hands over the list of users and the total stay length.
But you have to do that for every similar service and try and match up records. It would be a nightmare. Landlords would also create different companies/accounts to rent out the max nights per year. It's just not enforceable.
The tax office does this for tens of thousands of companies.
It can easily handle at most a dozen sharing sites. And it's trivial to prevent landlords from registering multiple accounts i.e. make sure no two landlords advertise the same address.
Relaxing the law in the manner you suggest would make it even more difficult to enforce than the law as it stood prior to this addition.