Actually, Google search has an ARPU of ~$256 per year [1] -- i.e. they're monetizing your eyeballs for about $20 a month. I applaud OpenAI: Please keep the service paid & ad-free. Thanks!
Stupid? If you had no access to a free search engine would you spend $20 a month on it? I sure would. It is also stupid to think that promoted results aren't a cost for you; if the search provider values it, there must be a cost.
The advertisers on Google would tell you otherwise. You are the product, ads are shown to you and you likely will click on one or more of them. Of course everybody says they don't , but the majority of people do.