Also, on a purely pragmatic note, capital is mobile. If you penalize the rich, they just move, and then the new system will stop class mobility.
Social mobility has very little to do with increasing your economic welfare in any absolute sense. It strongly favors countries with highly compressed wages and doesn’t imply much about ease of increasing income since it is only weakly correlated with that.
But yeah, some statistics indeed are just likelihood that the ranking order changes, or even self-reported...
It's like the definition of "middle class". Everyone thinks they're middle class. The OECD calls anyone with 75% to 200% of the average income "middle class". Classically the term means you are above the labour class but not noble.
AFAIK class mobility is measured by class at birth compared to adulthood (i believe as measured by net household wealth)