It would provide a gauge for the newcomers by racing in a field against experienced drivers. Long ago, that was the appeal of F2. You'd race against other youngsters in F3, then in a mixed field in F2, offering a real prospect of being able to impress.
- Increase the cost cap by 1 million to allow this (that's being generous as a single weekend damage usually wouldn't exceed half a million for a badly damaged car)
- Running rookies against a regular driver is a perfect way to gauge how good the young drivers are, and to put mid season pressure on underperforming regulars.
I don't think you understand the complexity of my concerns.
1. How does increasing the cost cap do anything? If the car is damaged, you have to produce replacement parts, if the car is not damaged, you can spend this money on something else and gain the advantage, regardless of by how much you raise the cap, thus there's an incentive to do everything to prevent damage, including things like prematurely withdraw a perfectly fine car from the race, pretending a mechanical issue and other less obvious things that prevent drivers from pushing 100%. Also there are parts that have to be in the car for multiple races, you're better off with as little wear as possible. It's in the team's interest to self-sabotage in these races if they're not taking part after the season.
2. I know it would be cool to have newcomers racing against the experienced drivers but that forces each team to choose one driver to take part and one to sit out. It could lead to potential unfairness, for example in case two drivers from the same team are in a close WDC race- maybe it could be advantegous to get more mileage in the car and more confidence and more setup testing or maybe it would be more advantegous to sit out and rest. You could try to combat that by making an even number of such races and mandating each driver to drive half of them but it leads to further complications.
I don't think the idea is very feasible in this form, F1 would need to take massive steps to make it workable.