This is such nonsense. First of all, there are absolutely people who come from dirt poverty and become wildly successful. Second of all, plenty of people receive lots of help from their parents and amount to precisely nothing. IMO it's fair to refer to your success as "self made" if you exceed the median success level of your class peer group by a substantial margin. If you immigrate from Africa with nothing, and you…
And there we go. That kind of attitude is why this trope was created initially.
The problem people have with "self-made success" trope is that the self-made success story of someone with severe disadvantages is being equated, on an astoundingly regular basis, with the success of people with substantial advantages. That's how Bill Gates and Arnold Schwarzenegger are both dubbed "self-made" successes, despite their rather different histories.
Even worse, it is being used to justify, defend and perpetuate inequality, by convincing everyone that the American Dream is that "anyone can make it". After all, if such-and-such person coming from dirt poor origins could become wildly successful, anyone can. Therefore, we must strive at all costs to avoid removing "incentives" that motivate people to reach for that elusive success.
Naturally, this will generate resistance, and rightfully so. Despite the endless propaganda that permeates the fabric of our society, the self-made success story of Bill Gates is not the same thing as that of John Paul DeJoria.
So yeah, I agree with you in one aspect: the self-made success is not a myth. It's something much worse -- it's propaganda.
It brings to mind that quote by Anatole France: "The law, in its majestic equality, forbids the rich as well as the poor to sleep under bridges, to beg in the streets, and to steal bread."