It's all a bit silly isn't it? The SGP already ran sprint races - 23 of them in fact.
This is quite aside from the fact that track conditions are going to change between qualifying sessions, so the session you're drawn in is going to influence the selection order for those that don't qualify for the 'sprint race'. Regardless of what's being claimed, it's not going to be the same for everyone.
Then there's the 'sprint race' itself. What happens if those four riders wipe each other out before the GP starts?
In MotoGP you've got far more riders in a race and you can't get them all on the front grid, so timed qualifying is one of the fairer approaches to lining them up, especially as you can put all the riders in one session where the conditions will be the same for everyone. Speedway - for precisely the reasons it takes place on a much smaller track and only has a small number of riders in each race as a result, has evolved a multi-race all-out sprint format.
If you really wanted to add some interest to practice, add some extra wildcards and have them race-off for a couple of places in the GP proper.