Person B -- the renter -- will pay more income tax, because Person B does not get to deduct mortgage interest while Person A does.
In much the same way, if Person A carries insurance all year and Person B doesn't, Person B will pay more income tax.
So yes, you do get "fined" for not buying a house. We just spin it as "encouraging the dream of home ownership" instead of as a "fine", a "penalty", as "the government holding a gun to your head and forcing you to buy a house", etc.