It would be 'fun' but I disagree it would improve the racing. All teams will change their cars into race setup and they'll all change them in similar ways which would maintain the status quo.
One other thing about the current Parc Ferme is that it forces the teams to make a compromise between Q and Race setup, and during the era of allowing DRS over the whole lap in qualifying was a really good example of that. The optimum wing flap for Q was different to that for the race and they had to choose. Unfortunately the FIA weakened the DRS rules.
No refuelling was also good for this - the car setup difference between full 160kg of fuel and quali/1 lap fuel was a balancing act and led to compromises in the car design and setup.
I would prefer for the optimum race setup and optimum qualifying setup to have an even larger difference, and retain the Parc Ferme rules so that the teams have to choose between race and qualifying speed. Then again, they'll probably all just choose one or the other end of the spectrum depending upon whether you can overtake at that track