I think it's a great idea, and I would say especially as early as prior to starting a Ph.D.! Since you mention talking about mathematics to a wider audience -- I think there's a side benefit to maintaining your own site and writing about your academic interests. If you write something regularly, like a short blog post or a short note on something you've been studying, you train yourself to become a better academic writer. This will become extremely useful to you in your Ph.D. It will help you in writing your future publications and a dissertation. The ability to write well academically is very valued by advisors because it saves them a lot of time in making corrections to your writing.
Like others who posted an answer, I also recommend hosting your page on GitHub since it's free and gives you a lot of leeway on what you can achieve. You can use Jekyll to convert markdown to HTML, it's super handy.
I also created my personal site shortly before starting my Ph.D. to showcase some of the past academic work, my scientific interests, and my fun side-projects. It has grown with content over the Ph.D. years, for example I've been adding links to my publications, links to the talks I gave, and I always keep a link to the most recent CV. This has helped many researchers over the years to find me and my work. It helps in science outreach and disseminating your research.
Best wishes for your Ph.D. journey!