"I just don't get it... who in their right mind would merge a web browser with a web server?"
Simple. It makes the browser able to accept incoming requests, which opens a completely new world of possibilities.
"And then try to put the lot in the hands of the same people who can't keep their computer patched/updated or otherwise safe from external attacks?"
Unite is not just a standard web server, it's tightly locked down. It's no less secure than, say, any browser.
"If I want a web server on my windows machine, I'll install one of the myriad Apache windows packages that exist already."
Yeah, but most people can't do that. There's nothing to beat the ease of use that Unite brings to the table.