Asymmetric thrust is balanced by rudder forces.

At full rudder deflection if you fly faster you get more correcting force: Fly slower and you get less. Minimum control speeds are the speeds at which the rudder forces just balance the asymmetric thrust.

Less thrust, and you can balance that with full rudder at a lower speed.

Obviously Vmcg has to be down to, at most, V1, or you couldn't control the continuing takeoff after engine out.

No point in having Vmcg much below that, for before V1 you are going to shut down the live engine(s) and there will be no asymmetric thrust.

Vmcg is certified in the worst case, and the real benefit of reduced max thrust when you are hot and high is that less rudder will be needed to keep straight