Yes - a first world problem.
Yes - Use whatever resources/ advantages/ abilities/ contacts you have.
Look at it more from the point of view of an employer. This is very broad, but assuming each level of wealth in society has the same spread of abilities:
you’d want a system that gets the best abilities for your investment- 400% out of 400% for ability:
if you have a system (unpaid internships etc.) that only gives high earners access, you aren’t getting the best abilities for your investment, 250% out of 400% for ability:
Like I said, very broad, that said, if money didn’t matter, I’d of course take all sorts of unpaid internships, become a class traitor, and be the first against the wall when the revolution comes.