Nice questions btw :)
I think this would be over complicated, and make a car/drivers true pace even less transparent.
I would like to make it as simple as possible.
As it is now, the tires wear a lot, which often makes overtakes lacklustre, because the driver being overtaken either had older tires, or harder tires. Worst case scenario, is that the faster car is just let by, because there is no reason to fight him, because their strategy is different – I just hate that!
I may be dreaming here, but I would like to see only one kind of tire. The number of tires should still be limited in numbers in practice and qualifying, but be limitless in the race. The tires should be able to be driven hard, and very close to the maximum, but you should still be able to melt/wear them down, by driving too hard, or having a bad setup. And very important: the tires should come back to the driver, if they are overheated, and allowed to cool down (unlike the Pirelli synthetic compound bull crap of today)
Boring tire management should be cured, as far as I see it, as it just wouldn’t pay off, and some racing should be possible.
The downside would be that cars would be further away from each other performance wise, but this is where the much shorter pit stops should be an advantage, and bring the performance closer.
I almost don’t care what the solotion is, as long as there is no more tip-toeing around to save tires.