I'd argue that running a webserver on a VPS/Raspberry/etc, with no logs, serving a static site or a wget mirrored version of that site is better - you still own

I'd argue that running a webserver on a VPS/Raspberry/etc, with no logs, serving a static site or a wget mirrored version of that site is better - you still own the site, but if you don't store any information of your visitors at all, in any form, there's no way GDPR will bite you.