Upward mobility is thwarted at first rung by bad decision making. To get to the middle class you have a 98%+ chance if you A.) Do not have out of wedlock children, B.) Do not use drugs, C.) Graduate High School, D.) Do not have a criminal record.
Moving from middle class to upper middle class requires the ability to defer pleasure further and avoid the financial traps of the middle class that keep people poor. 1.) Car payments, 2.) Credit Cards "for the points", 3.) Time Shares, 4.) Recreational vehicles of all types. 5.) Vacations, 6.) Financing standard living.
To go from upper middle class to upper class requires the biggest leap because it cannot be accomplished by preservation of capital, it requires ownership of a business providing a product or service, and then preservation of capital by buying appreciating assets with the proceeds. You cannot save and invest yourself to the upper class, the personal economic engine has to be big enough, larger than a salaried employee can achieve through wages alone.
The 40%-70% number you cite for lack of upward mobility, and for the sake of argument I'll accept, is going to be the people that have the inability to defer pleasure or exhibit self control in order to follow ABCD above and become middle class. (a very low barrier to entry)