"A good comparison of Wikipedia, since they are producing an educational product, is to compare them with modern universities, which are all "non-profit" as well. Look at many of the salaries at most colleges and universities, and you'll see many people making in excess of $100,000 per year, and athletic coaches that are paid in excess of $1,000,000 per year. Being classified as "non-profit" clearly does not mean that you have to pay your employees poorly.
And, of course, most universities also solicit funds and donations with the same agressiveness as Wikipedia as well. Got to keep that football and basketball program rolling, after all."
So because modern universities are poorly run and inefficient Wikipedia should be as well? Modern universities exist in their current form because they are largely government funded. The government gives credence to their degrees and therefore conducts the research it funds via the resources that universities produce. As a consequence most very expensive and cutting edge research is performed there and most of the knowledge related to it housed there. Even with the how available, that funding buys tools you just don't have elsewhere. Technology and open information is slowly eroding at that but it isn't there yet.
Modern universities, especially in the US, are a poor resource for education. They are slow to change and adapt. Throughout the vast vast majority of tech employers care far more about what you know, your proven track record, and your ability to learn than they do about degrees. Most employers, especially those with hiring managers who are promoted from engineering positions, would take someone with 10 years of related experience (especially who was still young) over someone with a masters. He'll eventually find one that will pay the same or only slightly less than they would a peer with the experience and the degree on top of it. Pretty much all would take someone doing a similar job at another enterprise of similar size for even two years. So tech is a long way toward already being there.
For science see the problem I mentioned above. For engineering... this is such a broad category, old school engineering fields often have entrenched degree mentality while newer and more flexible engineering areas have less of one. Maths? I'm not really sure this is properly considered a category so much as the common language between the previous areas. If we taught maths as the creative, easy, and flexible thing it is people working in STE would be not just using but developing maths on a daily basis.