What's the point of "CV available on request"?
Doing this does convey useful information: it signals that the individual has made a conscious decision not to post their CV online. If you come across this statement when looking for someone's CV you know not to waste more time searching. I think this is the real reason people do it, rather than any concern that people might otherwise not think to send an email.
Academic CVs can get quite long, listing conferences presented at, committees served on, etc. It's easy to see that some people would feel that the whole world doesn't need such a detailed record of their life.
- Actively ask another researcher for their CV,
I think it's more likely a non-academic would need this sort of thing. Here are some ideas why you might need someone's CV:
- A journalist or university PR person reporting on their work
- Preparing a biography (e.g. a conference introduction)
Or, as an academic, you might really like someone's work, and want a quick way to find all their papers. Google Scholar isn't perfect, especially when people don't curate it. Personally, I wouldn't email for a CV in that case, but someone else might.
Or perhaps they are open to being recruited by another lab or department or company, but want to know when someone is interested, rather than not knowing. Is this effective or a good idea? I have no idea.
Short answer: privacy.
When you're not looking for new opportunities, why should you expose your life to everyone who visits your website? Of course there are differnt views at that. Making the CV available on request is one of them.
In addition, it may not only be a concern about actual visitors, but an option to stop all kinds of bots from indexing your CV.