It doesn't contribute to a lack of social mobility. It is a perceived result of a lack of social mobility. And if your parents are in an income bracket, you are probably going to be in that income bracket. The only thing a high number of people getting help from their parents indicates is they might end up worse off than their parents, in income. But you'd need to wait until they've reached their peak earning years to know for sure.
It definitely contributes to a lack of social mobility. If you are competing with others for zero-sum access to the upper reaches of society and they get substantial assistance from their parents then you don't have as much of a fair chance.
The question becomes - how much of a factor does it play? I would think less than the intangible but non material benefits of having higher income parents (your upbringing, the lessons learned from your parents, their professional connections, a safety net that lets you take risk) but more than I would like to have admitted to myself a decade ago.
Exactly. My parents just paid for my sister to go and be a host at Camp America, with the explicit intention of it looking good on her CV. I think it's good she's doing it, and for them it's not a lot of money (as it's a paid role, just not paid enough), but it's not something that everyone can afford to do.
There has been a lot of criticism of unpaid internships for the same thing, notably in journalism in the UK. This is an industry entirely driven by unpaid internships, or jobs that pay well below what it costs to attend them in central London. As a result, journalism in the UK is a pretty middle-class dominated industry, which itself helps to perpetuate the cycle of low social mobility.
