You would use mod_rewrite to alter or remove information from an incoming URL.
But if you do that, you are removing critical information that the webserver uses to determine how to process the incoming request. That ".html" isn't just some sort of local filesystem extension, it's part of the MIME-typing process. It tells the server to look for and serve an HTML document, so if you remove the .html, the server won't work properly.
Going in the other direction, you can append an ".html" to incoming URL requests before forwarding them to
Tomcat, but if you don't code the rules correctly, it will append even to non-html requests such as
servlet and
JSP URLs.
It's not something I'd do just because ".html" offends me. Besides, people are used to it and generally only pay attention when they confuse an ".htm" with an ".html" or vice-versa. More generally, however, they're only manually entering a URL to get to the welcome page, where the welcome mechanism not only already knows the MIME type, it knows the page name.