I think the house market you live in is deeply distorted by some economic factors, which is probably law. It's not a normal market.
You say that it is somehow natural that rent costs more than mortgage (we assume no down payment) because the rented house is usually bought on a mortgage and the owner uses the rent to pay the mortgage. This is, again, the result of a deeply distorted market.
In a normal market, "rent" is the interest you pay on the capital you borrow (the house), while "mortgage" is the interest you pay on the capital you borrow (which you use to pay the house) PLUS restitution of the capital. In economic terms rent cannot be higher than mortgage unless there are factors which distort the normal behaviour of rational capital allocators.
If you take your mortgage "plan" you see that for each instalment there are two parts: the quota capitale and the quota interessi, they correspond to the share of borrowed capital you are giving back with that instalment, and the interest on the residual capital you borrowed (initial capital minus the capital you gave back with previous mortgage instalment).
If it were possible to buy a house with a mortgage and rent it for a sum equal to the mortgage instalment I would have no hesitation in doing it several times as this means that somebody (either the person renting or the bank lending) is giving me a house for free. Again in a normal market there is no free lunch and no free house.
I know this was possible in the US before the crisis but this was the result of distorting factors which were unique to the US market (maybe something similar happened in the Spanish market).
The idea that houses inevitably rise in value in the long run is at the origin of the last US house bubble and, like any idea behind any bubble, it is more based on wishful thinking and greed than sound economic theory and inevitably bursts leaving somebody with a hard lesson (and somebody else rich, naturally).