One thing to be aware of is that the range of incomes in many countries is much more compact than the US. If you define social mobility by the ability to move from the bottom segment to the top, it requires a much smaller change in income in most industrialized countries than in the US. For example, for the average person in Denmark to go from the bottom 10% to the top 10% of income requires earning a mere $40k more…
Imagine a country with a fiery economy: within a generation, real incomes will triple or quadruple, and at an equal factor across all income groups. Let's say also this country also has an incredibly rigid caste system, where you can predict that a person falls will fall within the same single percentile as their parents with 100% accuracy.
Your absolute measure fails to capture a situation that I think you'd agree shows very little income mobility, while the one you're criticizing succeeds at it. What I think you're getting at is that people can be much better off despite lack of intergenerational income mobility. Sure.
But people are looking for a measure that will capture the fact that some societies have parental income that's much more predictive of children income than other societies. It's an interesting reality that many people find problematic, and it has a real impact on other social systems--race, class, geographic mobility, educational outcomes, and elite networks--that are very interesting to analyze and potentially useful to understand.