Isn't this what REIT funds suppose to do?
You still haven't answered other problems, such as "What if the guy we rent it to is a deadbeat?" and "What if the guy we rent it to refuses to pay?" and "Who picks the apartment, and at what price?" and "Is a management fee paid to the guy who does the work of collecting and distributing payments?"
Also, I believe Kickstarter doesn't allow you to sell shares, only products. If you were doing this in the USA, there are all sorts of securities laws you have to follow; other countries are probably similar.
Also, what prevents you from Ponzi-ing it? I.e., take the money and disappear, or "buy" more apartments and use the profits to pay off previous investors?