Earlier quoted context omitted.
You say that, but I feel like it's a bit of a case of 'dress for the job you want'. Having a modern-ish looking site just gives off some signals like 'this is maintained', 'this has been deemed to still have utility in 2020' and 'the developer has some awareness of current UX'. It doesn't need to be flashy. Just a nice font, a header, centre justification, some spacing, a paragraph explaining what the thing is, a nic…
I had this thought recently--is there a class of website where being being un stylish and looking like it came out of an earlier era of web design gives the site more credibility?
It's not about aiming for an ugly UI, it's about getting out of the way and presenting a clean, simple, fast, functional page.
The designation brutalist web design has gained some traction. (I would have linked to an article on this, but ironically the page I found was offensively spam-ridden.)