First, blame the wonderful government (but not of Cristina) for having made a law that allows for people to not move out of a house that is not theirs. Same reason no one leaves property alone here for any length of time because if squatters get into your place you're screwed.
The prime reason to require a garantia is NOT for damages, but rather because of the fear that the renters will not leave (and that means not paying rent), rather will squat. If you have children involved, even worse.
Temporary leases (short term) are not outside the system (unless the owner simply isn't declaring earnings), but are indeed different under the law, and by law they are not supposed to be for more than 6 months, with (I believe) one additional renewal term. Anything longer and the contract, by law, converts to a long term lease. Short term leases make it easier for the owner to get someone out of their apartment if they're not paying - but again, if kids are involved it really complicates things.
There are indeed people who will rent their places long term without garantias. The first apartment I was in that was not temporary I occupied for a year. A friend of mine was living here but had to go back to the States permanently for work. He'd paid his entire two year lease in advance in lieu of a garantia and it was accepted - because he was a foreigner. I paid the monthly rent to him until the end of the lease.
I have another friend who spent months walking around the city and talking to various porteros to ask if they knew anyone who was willing to rent (mostly to avoid the commission of the real estate companies). He found anumber of apartments and finally found one where the person was willing to rent to him without a garantia - again because he was a foreigner.
I've never had the time to spend looking for apartments, plus my needs are bigger than most - we have 5 of us living together and I need an office. Much more difficult to find a lease without a garantia.
Also, you can indeed find places that don't require a garantia, but usually outside the city and in lesser-quality environments, or the living places themselves are very substandard (to me).
It's not impossible, but you can't just go down to the local real estate office, or look online, and have a large quantity of apartments to choose from. That's the real bonus of having a garantia is that once you have that, you can pretty much rent anything that you can afford - much like the majority of us are used to in the (maybe only slightly) saner outside world.