I don't see why they don't so what they already do in the Trophee Andros - in that series they have the main quali / races, and then have a separate shorter set of races in the electric cars. In the separate electric races, they have a combination of the drivers from the main series who are interested in competing, and also younger drivers that are hoping to impress and 'graduate' to the main series...
Think about the issue this year in F1 with a large number of 'test' or 'reserve' drivers at teams that don't have a race seat, under a setup with the main F1 race and shorter supporting race, the supporting electric races could contain a mix of back-marker drivers, convinced that they have what it takes to prove their ability or get back to a top team like Trulli, Kovi etc., test drivers such as Hulkenberg, Senna, Paffett etc., drivers that might have lost their seat recently but want to prove they should get another chance like Chandhok, Di Grassi etc. and potential stars of the future such as Mortara, Wittmann, Sims etc.
It would be something a bit different to the usual feeder series and lower level formulae...
I'd do it with no pit stops and keep the electric car races to literally 10-15 laps long and have it with spec cars. Lets see who out of that bunch of fringe drivers really is better than the rest, and if anyone really is a standout...

Favourite racing series: F1, Indycar, NASCAR, GP2, F3, Formula E, Trophee Andros, DTM, WTCC, BTCC, World Endurance... etc. etc.