As someone who works in the academy, I'm a big believer in academics having their own space on the web that provides context on their work and research and gives easy access to their growing body of scholarship. Academics should be Starting a Personal Website.
I'm also a proponent of thinking in public, and if anyone should be doing this, it's those of us who get paid to do research for a living. An academic is a Knowledge Worker. A personal website allows academics to do all of this and more.
For the academic, a personal website provides a dedicated space where they're body of scholarship can take on it's own life. Often, I speak with professors and scholars who rebuff the idea of a personal website based on the assumption that any attempt to showcase your work must equate to self-promotion. While I realy resonate with the desire to avoid any appearance of shameless self-promotion (and I do believe there are several Things not to do on your personal website), the entire purpose of scholarship is adding to the knowledge of others. A personal website is an excellent way to do just that.
Furthermore, this kind of website promotes discovery and dialogue with others who are also interested in your subject matter. An addedd bonus is that it does so without being tied directly to a social media platform. This means you own your work and you control where to post it. Having your own website does not, of course, mean you cannot use social platforms for dialogue, but it allows you to have a true "home" for all of your content.
Finally, if you truly believe in the work you're doing in the academy, I assume you hope that it benefits others. Having a place where others can benefit from your work is a key piece of that. Rightly understood, the purpose of a personal website for the academic is not self-promotion, but dissemination of your labor for the benefit of others.