A file like video.mp4 is really two things: a container (MP4, the box) and codecs (say, H.264 video and AAC audio, the contents). The extension names the box, not what is inside: which is why renaming a file never fixes it.
Half the conversions people need are really box swaps: a MOV whose contents are already MP4-friendly just needs re-wrapping, with quality untouched. The other half genuinely re-encode the contents: that is where quality decisions live, and where Flippy treads carefully.
This is also why converting to MP4 fixes so many playback problems: it is the box whose contents the most players agree on.