Absolutely.
The caveats are that if your family is rich/aristocratic class, then it probably matters much less and if your only options are mid tier universities, they might not be worth it.
Universities offer resources, opportunities, a network, prestige (it really does), and an environment where the latest trends are talked about and examined, easy access to the latest journals and the like.
I think a lot of people who grow up in the west don't understand what an impact western universities have on their societies. If you get a degree from a high tier university, many countries will let you in without much struggle, you are definitely in demand.
Where I went multiple people became bitcoin multi-millionaires because they were reading block chain papers when the BTC price was below a dollar.
I can't give such glowing reviews for universities for mid tier schools, but if you can get top 10/top25 on the world stage, I would say definitely.
Depending on how old you are, you could:
* Assume you won't go, and work on whatever you want to work on in the meantime
* Apply anyway, and consider going to the best one you get into for 1-3 semesters/quarters, to meet people for friends, spouses, cofounders, then drop out
Independent people know it upfront, they don't need a boss. Usually they then found a company. A friend of my started a business, direct after out studies. It doesn't have anything in common, what we both studied. Did he need studying?
Others are working, accumulate knowledge in their area, having a good opportunity and idea allowing them to build up a business.
So. To be able to answer your question properly, I need a definition what an independent person is. And some explanation, what a university has to do with an independent person.
But in my experience, people who don't attend university/ higher education are lack of experience in problem solving. So, independent, no university, but, sorry, stupid in terms of solving problems.
Re: University. Sure, if it's for learning (useful or not), I think it's a good thing. It's better it's out of curiosity and desire to learn, of course. Sometimes it's because you need that paper to enter regulated fields.