While your scenario is ideal it is not practical for alot of rentals. My rental is in a so-so neighborhood and rents for $1000. To find someone who makes $3000 after taxes to live there is never going to happen.
Is there a chance that if you were to update the place and make the inside nicer that someone would pay for it?
In the neighborhood of my rental in the city on the edge of were the highrises stop and grass and SFH begins there is MAJOR diversity. My same house not updated, lacking maintenance and basically uncared for might rent for half the price it is. In fact that is what the landlord does right next door. Not only is he cheating himself he is cheating the neighborhood.
Excuse me Eric but you have no idea what effort I have put into renting my house. I know more about this neighborhood then I think you will. Maybe I shouldn't say never bur unlikely that I will get someone making 3x the rent after taxes. As for the shape of my house it is one of the better ones in the neighborhood. While I don't get people with 3x times the salary I do get people who have good credit and all have been great tenants.