Mario Andretti agrees with you as well – your idea of a third car for new drivers reminded me of this interview with him:
(go to 1h06m21s, if it doesn’t start from there)
Lots of great drivers got their first shot at F1 in a third car: Gilles Villeneuve and Nigel Mansell as well as Andretti (Prost was offered one, but said no…)
3-car teams wouldn’t work as a permanent measure – just because Ferrari had one, McLaren and Red Bull would scream and shout until they had one too. But I love the idea of an occasional guest appearance – it would be good not only for young drivers like da Costa, Sam Bird or Kevin Magnussen, but also a chance for guys like Gary Paffett, or Dario Franchitti and the US drivers who tested an F1 car but never had a chance to race one.