The "Largest Portable Media Player MP4" is 7 inch (Wide Screen LCD) made from Korea, China and Japan!
One of them is a called "ACCURA 7010 GPS Navigation" - Yes, it is a 7 inch screen in-CAR GPS system, but you can play MP4 movie on it.
Another one is made by Pioneer (5.8 inch only), see the specification from the link:
I guess, nowaday, people won't just buy a Media Player for watching MP4 movie only anymore - I have bought an ACCURA 7010 which can play thousands NES games, watch MP4 movie and photo, listen MP3 music while using the GPS system at the same time!
It is same as mobile phone, if you check what an iPhone can do - it is not just a phone anymore...
If you still are using a 4 or 4.3 inch Media Player "MP4 Only" nowadays, it is a little bit out of touch from the high tech. gargets...