Since when citing a website you cite the way website was on a certain day, it would be good if Paperpile could save a PDF or screen capture of the website when you choose the “Add as a website reference” option. Personally I really like the way the Evernote web clipper saves and archives a simplified view of a webpage, but I find the process of creating an Evernote clip, getting a share URL and then entering that in Paperpile rather cumbersome. Both Zotero and Sente are able to save a version of the website directly to the citation and I think Paperpile should as well.
I think this is an already existing feature request made by someone else, but Paperpile also needs to save the access-date when doing this, in addition to the publication date, as it is required by many bibliographic formats.