To provide the same grip at a lower temperature the tyres would have to be softer, surely?
Just look at any race series with short sprints, like drag racing or hill climbing. You can push your finger into the single seater hillclimb tyres because, short of a couple of breif burnouts, they need to provide maximum grip possible from cold. On an F1 car those tyres wouldn't last a lap.
F1 tyres sustain their temperature due to the forces applied to them. Unless you drastically cut G forces and cornering speeds those forces won't reduce, and any tyre will still get that hot.
Unless there is some secret technology that nobody has released, a tyre that heats up quickly will be softer and last less time than one that heats up slowly. F1 negates this with tyre warmers. Removing tyre warmers will increase net time lost through a pit stop, making people even less likely to want to make any more stops than the minimum possible. Ergo, "save tyres".
I don't buy the cost saving argument, it a tiny amount in the grand scheme. The safety moans are also pretty weak. My concern is making a pit stop lose 45 - 60 seconds is going to kill the racing even more. Hence why I want them to stay.