Man of Honour
Exactly this, and it's so head crushingly obvious I don't know why it hasn't been suggested by the powers that be.The big problem now is the tyre compound rule.
What we really need are two tyres. One - a soft, grippy compound that can be coaxed into doing 45 miles or raced hard with for 20. Two - a hard wearing tyre that can run for 60 miles at a half decent clip or coaxed into running a race distance if you're prepared to sacrifice time on the road in favour of not stopping in the pitlane. Right now, there's actually no real difference in the two compounds that Pirelli bring - they're both knackered in pretty short order.
The thing is - drivers have to use both compounds in the race. So there's bugger-all incentive for Pirelli to make the tyre compounds all that different. The FIA has a very simple choice here - either mandate one tyre compound for each race, or allow free reign on tyre strategy. And in this era of cost cutting (where you can't test your car in-season, but you can spend a ****-load on finding a diffuser design that steals a march on your rivals....) there's pretty much no chance of TPTB allowing teams to use the tyre they want, when they want to.
There will never be any great gravitation from what we see now until they scrap the ridiculous 2 compound rule - because it puts everyone in the same boat.
Remember Pirelli are designing these tyres pretty much to order - they are giving F1 what they want. F1 wants tyres that degrade in a pretty spectacular fashion, and that is exactly what Pirelli have built.
People who've watched F1 for a long time will remember races like Paul Ricard in 1990 where Ivan Capelli and Mauricio Gugelmin ran at steady pace throughout on a no-stop strategy (IIRC) and Prost only just nailed Capelli shortly before the finish on fresh tyres.