Ok, so I was bored and I added very very basic HTTP support to vsftpd. vsftpd is now perhaps the only FTP server to have an option ftp_enable=NO. Basically none of the HTTP protocol is implemented, but it might suffice for someone who is super-paranoid…
The bits live at ftp://vsftpd.beasts.org/users/cevans/vsftpd-2.3.0pre1.tar.gz
I cannot use the name vshttpd, because bizarrely a Google search indicates it as taken: http://sourceforge.net/projects/vshttpd/. I do not know what the "vs" stands for in that case.
As usual, the feature will live or die depending on the level of user enthusiasm shown.