Outlook does do it, but that's because its a large scale desktop application not built with the probable limitations of mobile processing power.
The actual purpose of the junkmail filter built into outlook comes into play when one is sitting with an MS exchange server, the black and white list settings set by each individual user is also synced over to the mail server and in some cases is used as part of the global filtering. Its all part of an integrated system.
If your stuck with the awful mail server, then what you could consider is a mailbox wide auto-forward. Setup a secondary account for yourself with Outlook.com or GMail.com. On either of those you can setup a sending address, so it will basically act as a middle man, all outgoing mail will still be tagged with the email address of the POP account.
Your benefits in this will then obviously include the worlds most powerful spam filtering algorithms and the very battery friendly push services. I suspect that if you mail server is so useless at spam filtering that its using standard pull mail which then requires your phone to actually periodically check and fetch new mails.
Either way, this route will be far less painful and easily achievable over trying to find an app that will do this without negatively impacting overall device performance.