It's an interesting idea, but very important to get it right, it feels like this could end up being another positive feedback loop for top teams if not handled correctly. If its just simply a sprint race with a normal grid start, the top cars/teams will still get poles and naturally float to the top and stay there. I think if this new proposed qualifying has a system that has both rewards and consequences for the main race and/or championship it could actually be better than the current format, or even ride on the back of it, while benefitting bottom teams.
Example:
Quali sprint race is in championship order (first race of season could either be decided by an additional qualifying session of current format, or be based on last year's results, perhaps new team(s) being rewarded a front row slot for a kick start). Small amount of championship points are rewarded (maybe something like 5-3-1 for podium order or 5-4-3-2-1 for top 5), and then main race is in reverse qualifying order. This way there's an incentive to go for top of quali, but with more work to do to get big points in the main race.
Alternatively, quali starts in reverse championship order, and then sets the grid order for the main race, everything else from above the same. Either of these could make Monaco or Spain very interesting.
Downside of first order could be top teams artificially going slow in the sprint race to lock top spots in the main race. Reverse championship+reverse quali would seem to have the most "equalization" processes, however I feel like part of the allure of F1 is the outright performance of the cars highlighted, and not having the fastest at the front as a reward for pace at any point in a race weekend could take away from some of the spectacle.
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While typing that out I came up with an idea of combining the current system with my "theorized" new system, which could be awesome (in my head). "Traditional" qualifying (the Q1, 2, and 3 system we all know) decides the order of the quali sprint race, which has the small theoretical championship point reward (5-3-1 or 5-4-3-2-1). Results of the sprint race set the reverse order of the main race.
That still leaves an opportunity for top teams to fudge the sprint for ideal main race grid spots, so maybe adding in an additional pole position point could keep teams a little more honest? Also a difficulty with this system could be the additional engine mileage, so maybe F1 could open up the allotment to four per team before penalties come into play.
No matter what happens, I just hope there's something in the system that lets bottom/struggling teams make some sort of gain.