From testing, .html stripping does work as intended. What doesn’t (seem to) work is stripping the extension when a path ending in .html is entered manually into the address bar (i.e./page1.html isn’t redirected/rewritten to /page1.) I don’t know if this is intended or not (ping @hillary for possible clarification.)
Best practice IMHO is to not use extensions in links either internally or externally. So instead of having
<a href="/page1.html" title="Page 1">Page 1</a>
<a href="/page1" title="Page 1">Page 1</a>
and add a <link> element with rel="canonical" e.g.