Besides that, making your own website is rewarding in many other ways - Being creative, getting thoughts out of your head, pinning down certain arguments you tend to repeat, etc.
…does not always work. When I give people a link they can't click on, they type it in the search bar. And not even in full, they tend to strip the http://www and .com ends. And you can't click on a piece of paper, which is where my CV typically ends up on.
Last week, I interviewed with someone who said he googled me. All he found was a "little GitHub page". My full name ranks my personal web site first or second on every search engine I've tried, yet he couldn't find it. Is the Google bubble that strong?
https://duckduckgo.com/?q=Loup+Vaillant
Try giving them a QR code instead.
But otherwise: If you apply for an job, say in finance, you'll be asked for a resume, because people can't be bothered dealing with information that's extraneous to what goes into a resume.
If you apply for a job as a coder, you'll be asked for a link to a github repo, because people can't be bothered with looking at anything other than your code.
If you apply for a research role, you'll be asked for a link to where your publications can be found, maybe on researchgate, because people can't be bothered with looking at anything other than your peer-reviewed publications.
Do you see the pattern here? It's another example of the balance between information and attention shifting towards too-much-information/too-little-attention. -- And personal webpages aren't good at dealing with the too-little-attention part of the equation, so there is rarely a demand for giving people information about yourself in the "free form" style.
The second aspect you mention: If you produce some webpage content, you can always decide whether you want to see it as a diary and not put it up online, or whether you want to see it as something that should be out in the public, and do put it up online. It seems to me like a contradiction to prefer putting it online, but then not to care about whether it actually gets seen or not. (Especially considering that one gets into a lot of liability everytime one puts something up online).
In my experience, this is not true. I setup a website to describe software projects, and my role in them. It was, per my current boss, a key factor in getting an interview. Browsing github repo's, imo, is much more bothersome than reading a well crafted project page.