Assumed facts not in evidence.
People tend to conflate relative mobility and absolute mobility. Relative mobility is a zero-sum game, if you move from the first quintile to the second, that means someone else has dropped downward. Absolute mobility, by contrast, measures how your income compares with your parent’s income. E.g., assume your parents make $20,000 a year and you are in the bottom quintile. If you stay in the bottom quintile, but make $25,000 a year, you’ve experienced absolute mobility but no relative mobility.
The largest decline in absolute mobility occurred between 1940 and 1964, so rather than blaming Reagan, you should be blaming Ike-JFK-LBJ: "On average, 92% of children born in 1940 grew up to earn more than their parents. In contrast, only 50% of children born in 1984 grew up to earn more than their parents. The downward trend in absolute mobility was especially sharp between the 1940 and 1964 cohorts. The decline paused for children born in the late 1960s and early 1970s, whose incomes at age 30 were measured in the midst of the economic boom of the late 1990s [i.e. early GenXers did relatively well]."
As for the supposed decline in relative mobility, even that isn't clear: "I show that accounting for race and measurement error can double estimates of intergenerational persistence. Updated estimates imply that there is greater equality of opportunity today than in the past."