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It doesn't have to be high intent all the time though. Chrome itself is "free" and isn't the actual technical thing serving me ads (the individual websites / ad platforms do that regardless of which browser I'm using), but it keeps me in the Google ecosystem and indirectly supports both data gathering (better ad targeting, profitable) and those actual ad services (sometimes subtly, sometimes in heavy-handed ways like via ad blocker restrictions). Similar arguments to be made with most of the free services like Calendar, Photos, Drive, etc - they drive some subscriptions (just like chatbots), but they're mostly supporting the ads indirectly.

Many of my Google searches aren't high intent, or any purchase intent at all ("how to spell ___" an embarrassing number of times), but it's profitable for Google as a whole to keep those pieces working for me so that the ads do their thing the rest of the time. There's no reason chatbots can't/won't eventually follow similar models. Whether that's enough to be profitable remains to be seen.

> Search is all about information retrieval. AI is all about task accomplishment.

Same outcome, different intermediate steps. I'm usually searching for information so that I can do something, build something, acquire something, achieve something. Sell me a product for the right price that accomplishes my end goal, and I'm a satisfied customer. How many ads for app builders / coding tools have you seen today? :)