> valuable traffic
What's the value for the website maker in these? There's user value to it (rather than just value for Anthropic/OpenAI) but the whole point of these bots is to make sure nobody ever needs to visit your website.
Tons of people click from ChatGPT! It's now the top referrer on most of my websites, and seems to be on path to overcoming Google soon (a ton of traffic from Google has vanished since the AI Overview rollout...).
In my case this is the main source of registered users. If a user is engaged in a discussion with chatbot and gets the recommendation from it his engagement is higher. For example, in my system, a user has registered and within one hour used the system 7 times and stayed active while for registrations from Google I can observe zero-activity accounts.