They don't have to do that today, though. Remember original Google? Or original Gmail? Neither had prominent ads for the first few years, a couple decades later the ads are everywhere.
OpenAI isn't burning through tens of billions of dollars every year on its free tier for charity. It will dial up the advertising knob (and every other knob) to 11 the moment the cash starts to runs out.
How is it different than Google Summaries or AMP or any of the other ways Google tried to keep people from actually visiting the websites that drive all of their traffic.
I usually do the same, but not always. And I believe clicking through is a behavior of a minority of people and interactions, judging by the click through rate drops sites have seen recently. (On mobile at the moment, so apologies for not grabbing a source for the rate drops sites.)