I've never seen a 60 amp subpanel. Most panels seem to be rated at 70, 125, and 200 amps. When someone says to me a "60 amp subpanel", I'm assuming they want a 60A feeder to a subpanel. If you want a 60A feeder, and can use 75C terminations, then you need #4 aluminum. If you can only use 60C terminations, you are still fine with the same wire but your calculated load must be limited to 55A. If people aren't doing calculations (e.g. typical residential install) then having an ampacity equal or greater than the breaker rating is a good design (use the 65A wire).
I don't know how you could ever use #6 al to feed a "60 amp subpanel". It is limited to a 40A or 50A breaker depending on termination temperatures, and perhaps even less if there are deratings to apply.
The code book cannot be as you wish because wire ampacities don't land on nice 40/50/60 amp boundaries. They are what they are, and then when you add derating factors they get even more off from standard breaker sizes. The NEC tables can't know your ambient temperatures, bundling, etc to give you a simple answer.