ffmpeg -i foo.mp4 -c:v h264_videotoolbox -b:v 1600k foo_out.mp4
On macOS, this uses hardware acceleration to reencode a video at a lower bitrate. My macbook is from 2012, so this does make a notable difference. There's also "hevc_videotoolbox" for H.265 if your machine supports it.
And no, they won't ever get rid of categories. It's just that the phone variants of the site are very heavily geared towards a specific type of reader, at the expense of editors or other types of users. They have been trying to address this over incremental updates though, such as now showing talk pages.