Hi johnSteve,
The answer is technicaly yes and no. From a shared host environment the answer is yes.
You can setup .html files to be server parsed, however it takes up more server load to parse every single html file for server side includes and therefore we ask customers to use the .shtml extensions.
I am not real familar with all the technical aspects of SSI and how to parse the .html extensions, but here is a link that you may find helpful.
http://www.javascriptkit.com/howto/htaccess4.shtmlPat
