MP4s aren’t as supported as GIFs. Even if you convert them they’ll be heavier than LICEcap’s results because of the MPEG compression artifacts
That's barely true for H.264 and it is a much worse format in every other way. Effective quality is higher with modern video formats because the lower data rates afford higher resolutions and higher frame rates. Even the LICEcap demos show that.
It's a neat tool, the user interface is really cool, but it would be better in a different format.