I certainly understand that this might not be top priority for Paperpile, esp. given its academic roots and focus, focus on a mobile app, and small staff. I am an entrepreneur and am constantly researching new topics for presentations, reports, white papers and other documents. Many of the ideas that I pull come from non-academic sources, and I get a tremendous amount of research and inspiration from web-based sources. If a site changes or pages disappear, the value of citation is zero. It is currently a cumbersome process to save a page or print it into pdf format, then add the citations. This is clearly an area where Evernote is exceptionally strong; however, their system is not at all geared to reference work, and I frequently get lost without details on document sources.
Adding the ability to pull in html/web-based material would make Paperpile a killer app outside of the academic world.