Note that Firefox only uses OpenH264 for WebRTC video, not the <video> tag. OpenH264 only supports H.264 Baseline Profile, not the Main or High Profiles commonly used for embedded video. Also, MP4 videos often use AAC audio, which Firefox can't playback.

Cisco paid for the MPEG-LA licenses on that. Back in 2013, they probably had to, but more patents have expired since then, and it's probably out of patent now, unless they put in extra stuff like N-channel audio.

If/when patents are gone, you could legally use and distribute self-compiled binaries, since source is already under BSD license.