That is not really a massive amount of tyres however. It is only in the region of a 20% increase and the bigger teams will do anything for an edge. As per the Pirelli coverage pre-race the other week, all tyres are shredded after each weekend whether they are used or not anyway and a brand new fresh set is made for every driver in the next GP. Replacing 3 sets from the mix of compounds with qualifying tyres would not really upset the balance of waste generated.
Dont think your maths is quite right. I think the teams have something like 13 sets of tyres per car per weekend (someone will clarify the exact amount). Assuming the minimum of 3 runs in qualifying, plus 2 sets to practice on, that's an additional 5 sets per car, or 38%.
But thats the minimum of 1 run per Q session and 2 practice sets. If we get more realistic and expect 2 runs per session, and 2 sets per practice session on Friday to setup the car, thats 10 sets of tyres extra, or a 64% increase.
And it wont mean a reduction in the number of other sets either, as they wont go the distance. They still need enough sets to get through all the practice sessions and the whole race. At most they might drop 1 of the standard sets.
Remember the FIA dropped the number of tyres available to the teams this year (15 to 13 per car, I think?) on grounds of being 'Greener' and reducing transportation costs for the tyres. There is no way they would get an increase to 25 sets through the PR department.
Also, as has been said, without competition between manufacturers, what's the point?
EDIT: actually, I like the whole "take all 4 compounds, let them use what they want" idea. But unfortunately again that will fall foul of the Green agenda. You are then literally talking about taking double the number of dry tyres to every race, with a massively increased proportion of them never being used.
