Not sure what I think about double headers and standing starts one day, rolling the next.
It could be pretty limiting for any team who struggles for spare parts. Heavy damage in race 1 or engine failures could get pretty expensive to be dragging the extra parts around "just in case".
You might see a few more teams/drivers not starting races due to lack of money/spares to repair damage.
It could also be quite decisive championship wise for similar reasons - I mean I'm sure Penske and Ganassi will have more than enough capacity to bring the extra parts with them, but even for them it could be a bit of an ask to strip and rebuild cars (if that scenario came about).
Speaking of which, what are the rules in Indycar on spare cars?
In other championships that feature multiple races, its quite a common sight to see competitors miss the later races due to accident damage. Especially in the WTCC and BTCC. Similar to Indycar at the moment, both series also recently switched engine regulations which resulted in some teams suffering entire race weekends being unable to start due to duff engines blowing themselves up early on. Expensive both in terms of the championship and having to lug around a spare engine "just in case"!
Personally I don't really think the GP-length races in Indycar and F1 should ever be "double-headers". Everything in the weekend should be a build up to a climax in one race. Having two races splits the excitement and half of the result is already decided.
Multi-race weekends work fine for touring cars because they run shorter races and they can take more damage. Taping up a bumper so that the car is legal is fine, you can't really do that so much in open wheel formula.