Hello Martina,
this argumentation is of course also very understandable - as a landlord, I would clearly prefer it that way too.
However, since I do not know the landlords of the two, I just wanted to point out the risk of violating the tenant’s obligations under the contract. There have been reports of landlords who have responded to such a "solo action" by the tenant with a warning.
Keyword: "How am I supposed to know what it looks like under the new wallpaper and whether the mold was actually removed professionally?"
So it really depends on the landlord and the contact with him.
Regards,
Dirk