Once again, mp4 SHOULD be associated with the media Player. There is nothing else to set it to. Even with no default set you should not be prompted how to open the file, you should be prompted how to download it.
The browser should not launch the media Player. The browser should launch Downloads and when the downloaded file is tapped, Downloads should launch the Player.
I've read all over and I'm now convinced that this is an Android issue, not an app or settings issue. Even apps designed to download files never get a chance to download .mp4 files, they are sent straight to the Player apps as a web path instead of being allowed to download as with any other file.
Basically mp4 links are broken under Android and they need to be treated as discrete file for downloading. Anything that the browser itself cannot open should be offered as a download, with other Players / Viewers as secondary options.