I’ve reached the same conclusion.
The distribution rate is very likely a two-ended bell curve on tokens to not only make it hard to finish the rarer medals, but also to not make it too easy to medal Common cards (unlike weapon upgrading).
When the devs create new systems, they do so with the goal of a long-term viewpoint. Obtaining medals and medalling troops is supposed to take a very, very long time to achieve. It’s the next Zuul’Goth-like chase. And unlike, previous long-term goals, the devs have created a system where they can create new mythic or similarly super rare medals for players to chase at their whim, forever and ever for the remainder of the lifetime of the game.