That’s fine. The point for website owners isn’t to make money, it’s to not spend money hosting (or more specifically, to pay a small fixed rate hosting). They want people to see the content; if someone makes the content more accessible, that’s a good thing.
You ignore the issue of motivation. Most web content exists because someone wants to make money on it. If the content creator can't do that, they will stop producing content.
These AI web crawlers (Google, Perplexity, etc) are self-cannibalizing robots. They eat the goose that laid the golden egg for breakfast, and lose money doing it most of the time.
If something isn't done to incentivize content creators again eventually there will be only walled-gardens and obsolete content left for the cannibals.
AFAIK, currently creators get money while not charging for users because of ads.
While I don’t blame creators for using ads now, I don’t think they’re a long-term solution. Ads are already blocked when people visit the site with ad blockers, which are becoming more popular. Obvious sponsored content may be blocked with the ads, and non-obvious sponsored content turns these “creators” into “shills” who are inauthentic and untrustworthy. Even without Google summaries, ad revenue may decrease over time as advertisers realize they aren’t effective or want more profit; even if it doesn’t, it’s my personal opinion that society should decrease the overall amount of ads.
Not everyone creates only for money, the best only create for enough money to sustain themselves. A long-term solution is to expand art funding (e.g. creators apply for grants with their ideas and, if accepted, get paid a fixed rate to execute them) or UBI. Then media can be redistributed, remixed, etc. without impacting creators’ finances.
Because I as an user would be glad to have "free sites only" filter, and then just steal content :))
But it's an interesting idea and thought experiment.