It really depends on what kind of mobility we are talking about. The wealth and influence of the individuals I mentioned is pretty much impossible to reach unless you have optimal initial conditions. As the saying goes, the easiest way to become a millionaire is to be born a billionaire. Even if you are born a mere millionaire, you can make many more attempts at becoming a billionaire than a person who needs to work in order to have dinner.
There is a lot of statistics that point that current levels of social mobility are on par with feudal England and, while a modest improvement in conditions is very achievable for those who aren’t born in the most unforgiving situations, the remaining possible paths are very much closed.