It depends on what you're trying to measure by "economic mobility" though. I can think of valid reasons to want to know the percentile change between a person and their parents, irrespective of the absolute value difference, and reasons to be interested in the different-but-related measure of absolute change in income/quality of life.
It's generally better to start with the question "what do I want to know?" and then looking for a suitable statistical framework that will answer that question, rather than starting with a ready-made statistical analysis and then trying to use it to answer arbitrary questions.
I can think of valid reasons to want to know the percentile change between a person and their parents, irrespective of the absolute value difference, and reasons to be interested in the different-but-related measure of absolute change in income/quality of life.
Sure, but when comparing nation A to nation B, it's generally more interesting to look at either the absolute dollar difference or some relative quality-of-life measure (you could call the latter "class", I guess). Folks moving around within a tightly distributed income distribution don't really gain or lose much of either, relative to someone in a society with larger disparities.
It's generally better to start with the question "what do I want to know?" and then looking for a suitable statistical framework that will answer that question, rather than starting with a ready-made statistical analysis and then trying to use it to answer arbitrary questions.