"You couldn't possibly pay the massive amount of people making edits today"
That assertion is worth looking at, because the number of people editing Wikipedia is actually fairly small. The English Wikipedia's core community for example is a little over 3,000 people; another 30,000 people or so make perhaps one edit a week.
The total number of edits made in all Wikimedia projects together (Wikipedia, Wikidata, Wikimedia Commons, Wiktionary, Wikisource etc.) over the past 15 years is about 2.5 billion at the time of writing. That sounds a lot, until you remember that Google's ad revenue alone is $17bn a quarter. Google's Wikimedia-based Answer Boxes and Knowledge Graph panels are an important factor driving that revenue. They train you to look at and click in those areas of the search engine results page where the paying ads are.
Now, if Google gave just a single day's ad revenue (about $200m) to Wikipedia editors, each Wikipedia edit would average out at $200m/2.5bn = $0.08. For a Wikipedia editor who's made 150,000 edits over the past 10 years or so, that would be $12,000.
And while Google is the biggest player leveraging Wikimedia content to get eyeballs on paying ads, they're by no means the only one. Bing, Facebook (which contains a complete copy of Wikipedia) and others do the same.
That's not to say that I couldn't imagine other problems arising, along the lines you are describing, but given the scale of the economies involved, the problem isn't that there isn't enough money in the system. The people who profit most from "free knowledge" are mega-rich corporations, and they're keeping their profits to themselves.