University and other structured learning environments can be useful for some, not all.
Early on I tried to get ahead without higher education qualifications, but got stuck, so had no option but to eventually do a degree.
University and other structured learning environments introduced me to subjects and ways of thinking which I would not have look at anything like as quickly, if I had stayed self-taught e.g. OOP, RDBMSs, Networks, etc. You can also get detail on areas which do/don't work, so you know why, can recognise them, and have good reasons to welcome/fight them in future e.g. several project management and development methodologies were so hyped, but crashed and burned :)
Degrees are only sensible if you pick something you are interested in, are smart enough, and they provide new insight and knowledge you can use; otherwise they are pointless. Governments need to realise that most people don't need to go to university, because this only leads to excessive drop outs, useless graduates, and a pointlessly expensive education arms race; proper apprenticeships and vocational courses would be far more valuable for most people.
Yes, the right degree matters; early on I saw what a mess a recent Geology graduate made of some commercial computer work because he bluffed a position, but was clueless at development and problem solving, so bailed; I a recent Computer graduate promptly sorted out the software and got it working excellently; I left later, to get more interesting work and money.
Just because there is loads of information on the internet doesn't mean you can learn everything alone, there is still a huge amount of rubbish and deception there too; a lot of relevance, and comprehension still has to be learnt from interaction with other people, and online interaction may not be adequate to provide this. It takes a long time to form good mental BS filters and stuff still slips past!