I liked the idea of the logarithmic speedometer for practical purposes, but for theoretical purposes I'm thinking that an x^2 speedometer would be nice. This speedometer would have the position of the needle proportional to the speed squared. This would mean that the numbers on the low end of the scale
would be crammed together much tighter than a linear speedometer, and the large speeds would be spread out. This isn't very practical, because it makes the problem that the logarithmic speedometer solved even worse than it was originally, but this speedometer has a few useful characteristics.
One is that the speed of the needle is proportional to the power being produced by the engine. This is useful for those trying to get max acceleration from their car since if they shift before redline and the speed of the needle drops, they know they shifted too soon. If the speed of the needle increases when they shift, they probably should have shifted sooner. (not accounting for time wasted while shifting and the fact that they really ought to be looking at the track, not the speedometer, while this is happening).
Another useful feature is that each unit of distance along the speedometer represents the same amount of kinetic energy. This would help people realize that although doing 65 in a 60 zone is speeding by only 8.3%, and doing 35 in a 30 zone is speeding by 16.7%, the car doing 65 has alwmost twice the excess kinetic energy as the other car.
Therefore, since this idea has appeal for the racing crowd and the safety crown, it should have no problem being widely adopted: making life miserable for everyone who just wants to know how fast their car is going without squinting at the dash...