Looking for POP3 Webmail client that stores on local webserver

Most Webmail clients are IMAP (leaving messages on the mail server). Those that offer POP3 also leave messages on the server.

Instead, I’m looking for a Webmail client that uses POP3 to actually collect email and remove it from the mail server, like a traditional desktop email client would do. It would store emails on the local web server file system (or database). Recommendations?

Alternative: Instead of the Webmail client having to talk to the email server at all, I could set up a cron job to fetchmail to an mbox file (or similar) on my web server. Then, the Webmail client would just be configured to read from that mbox. Any suggestions?

The benefit to this approach is that emails are handled by a modern web application, rather than languishing within the constraints of an email server. Notice that Dreamhost forces emails to be archived if the inbox grows too big. This would alleviate that burden; the mail server’s inbox would be frequently cleared, and emails can live forever in a comfortable, roomy web server.