This is clearly not true; Wikipedia isn't ad supported and is incredibly successful and prolific. You can use educational tools like WolframAlpha freely and pay (using a normal subscription model) for its more advanced features, no advertising required. KhanAcademy is completely free (yes I know they host many of their videos on YouTube; that's a minority of the content on KA these days and I suspect would be a relatively minor hosting cost at this point based on how tiny and easy to compress their video presentation style is).
The internet would be different, yes. We'd probably see much less of a gold-rush than we've historically seen. I think it would still be just as much of a treasure in learning and communication as it is today though.
Wikipedia has a somewhat unique architecture in that it's mostly text and most of that text can be cached. This is also true about blogs and sites like HN and Stackoverflow, but not social media sites, search engines, messaging services, video and image hosting sites etc.
Most Wikipedia visitors use an ad-supported search engine to find articles. All that Wikipedia itself needs to do is to find the URL in their cache and send the pre-rendered HTML page. For many requests, there are no SQL queries to execute and there's no PHP Wikimedia code to run, it's just finding some HTML in a glorified key-value store. There's relatively little code to run and relatively little bandwidth required, so the cost-per-user isn't that high. There's also very little technical innovation, the core problem has been solved and the community is just adding more content. Same goes for HN and Stackoverflow.
Not all websites can operate that way. Search engines need lots of compute for indexing and search, and lots of developers to fight SEO spam. Not all searches can even be cached, "nearby Sushi restaurants" needs to return results based on your location etc. Social media websites spend a lot of money on moderation, and all their users are logged in, giving them far fewer opportunities for caching. Pushing a Taylor Swift tweet to all her followers in almost real time is definitely no small feat. Messaging apps need to deal with a lot of push notifications and a much higher proportion of writes to reads (when compared to Wikipedia), also moderation, fighting bots etc. Video and image hosting websites need much more bandwidth and storage (and possibly compute for transcoding), and those aren't free.
The non-profit, no ads, free-for-all model just doesn't work that well for this kind of platforms.
> Most Wikipedia visitors use an ad-supported search engine to find articles.
Because Google spends billions of dollars contorting and manipulating the entire internet ecosystem to only work with Google's model of the internet.
There are really simple solutions how the internet can be ad free and function much better than it does today in terms of serving information people. The internet is far, far worse due to the financial incentives involved
In an alternate world where ad funded sites never took off...
Taylor Swift could publish an RSS feed, or pay Twitter since it's basically a marketing channel for her. Messaging apps could have been p2p (and maybe ISPs would've had a reason to get ipv6 working since otherwise you'd hear "IM doesn't work on Cox" etc. Or maybe ISPs could provide federated chat gateways like they did with email). ISPs might bundle hosting (they used to), or Microsoft would have had a reason to have built Personal Web Server into something everyone uses today. Maybe people would share viral videos they liked on something like gnutella using magnet links from forums.
It might not work for companies trying to corral the entire world onto their platform, but maybe that model isn't very good.
The internet would be different, yes. We'd probably see much less of a gold-rush than we've historically seen. I think it would still be just as much of a treasure in learning and communication as it is today though.