Slow(ish) hosting for a very small client. Very static homepage – make the move to static html page instead?

I have a website running on – which is OKish, but google page speed insights could be better. I’m thinking about making it even better by just creating a static HTML generator from the homepage code, and every once in a blue moon when the client updates the website, he can generate static HTML and upload it (all automatically via a button) as the homepage.

Without loading all the WP core, it should be way faster. The question is what are the disadvantages with this approach? Do you have a different suggestion for some slim WP core?

P.S. In addition to the HP there is a client area, but the most important thing is to make the homepage SEO friendly. Anything else is not indexed anyway.