I think some people are confusing what they want.
Remux a video file's container extension (like .ts) to another, like .MKV or .MP4 is just taking the video and audio tracks untouched, and re-inserting them into the new container extension, the only thing changes is the headers etc for the file extension.
I do this when needed, to like when i trim out commercials for a file i want to save, using MKVToolNix. This is remuxing.
Re-encoding, or converting the file, this means you are reprocessing the video and audio tracks, which no matter how u do it, degrades quality. This is for when one wants to take a video file (no matter the extension) and make it into a different video codec format. Like taking a mpeg2 video track and a AC3 audio track, and encode it into a mpeg4 H264 and MP3 audio track file....and the final file can be a .ts, .mp4, and .mkv...doesn't matter. Or convert a mp4 H264 to HEVC H265 etc.
I like and much prefer that Channels leave the files as they are raw from the tuner source.
Emby, does have a convert to "portable" format where it will transcode the recording on the fly to make it a mp4 h264...but it had its issues and never was very reliable.
And also, i noticed that only certain channels were still mpeg2 while most of them were all already h264. (from the HDHR Prime Tuner i used back then)