It's certainly an understandable request. Even users who have "done nothing" and were happy with leaving their boards at phpBB 2.x or 3.0.x are here now, "forced" to upgrade yet again. Since even though they
"stood still", their hosting provider and PHP versions did not.
We did help someone use WGET to walk their site
and download every page as HTML. The scenario at the time was "make a backup of the site even though the site owner is AWOL", and no better option existed. WGET is a bad solution for that scenario, because even though you get an HTML download of every walked page, their intention was ultimately to build another phpBB site with that data, and parsing from HTML back to phpBB is hard.
But in your case the HTML-rendered page is the end goal. You might need to do some minor massaging to the downloaded HTML data to help build a static site you can tweak and manage CSS display of and similar, but "the hard part" was already done for you by phpBB in rendering the posts (along with the BBCode, etc.) to HTML. Of course the pages are not agnostic, and still "look like phpBB" rather than some generic information export. But with enough "Search & Replace In Files" of your favorite editor, maybe even that changes.