Its a more sensible suggestion than customer cars, as the deveopment of the car remains with a single team. Customer cars would result in half the grid having testing spec machinery they would then struggle to upgrade.
There are a lot of good points about the 3 car teams, but for me there are 2 major points it would need to cover:
1. ALL teams must run 3 cars. Having a situation where some teams run 3 and some run 2, where some people score points and other don't, yet still count in the standings is going to just confuse and anger fans. The FIA are clearly worried about confusing fans, and unlike some of there recent knee jerk reactions, this would genuinely cause issues and should be avoided. So all teams run 3 cars, all cars score points.
2. Costs MUST be brought under control. I will be the first to admit I don't know how to do this, but they simply have to in order to get 8 teams on the grid capable of running 3 cars. Of the current 11 teams I think we can safely say Caterham, Marussia and Sauber would not be able to run 3 cars. Then Lotus, Williams and Force India must have to take a serious look at the books. And then Toro Rosso. Would Red Bull need to run a junior team if they have a 3rd car at RBR? I doubt it. I doubt it even more when you consider 2 teams would mean 6 cars and 1/4 of the grid?
Personally, right now, I think while better than customer cars, it wouldn't work. There are too many other things that need fixing first.
Actually... is this the FIAs knee jerk reaction to teams looking like they might leave? So teams are leaving because they can't afford to compete, and the FIAs solution is to... make F1 cost 50% more to compete in!?