For me the primary benefit of a contact form is obscuring its destination (or piping it into a CRM or ticket system).
Search is important. But other functionality includes things like content embargo/scheduled publication. Or multi-author systems, where not everyone who is writing the content should be doing any damn thing with CLI tools or Git or any such thing), and where there might be editorial approval before it is posted.
Analytics: again, this is something that I personally believe should be achieved in aggregate on the server side, not in JS trackers.
Most simple business brochure sites do not need much, but most simple business users like a control panel they can log in to.
I do not have _any_ customers I'd deploy a static site generator to. It's just not going to happen without an online frontend (or something like Publii, maybe).