I think it's not about re-broadcasting, but about providing the show in a better format. The originals were shot on 35mm film, and then that was "mixed down" with the visual effects to some lower-definition format (maybe SVHS, but I'm just guessing) and the result sent to TV stations to broadcast.
To make a high-definition format (e.g., blu-ray or HD streaming) they'd go back to the original 35mm masters and re-convert them. But then all of the visual effects had to be re-added on top.
There are various articles that mention quality issues with the remastering:
I'm not sure about Babylon 5, but I believe TNG was shot on film, but the effects were all done at broadcast resolution due to cost. This meant that when they released the DVD version, it was not difficult to create HD versions of all the "real" footage, but the effects were all in standard definition, so they looked awful. For the Blu-ray remaster, I believe they redid all the effects with modern CG, so they no longer look like crap.
Both ST:TNG and B5 took their original source material and brought it down to SD and added the visual effects in at that level. So, we still had higher resolution original source material, but it had no effects in it. And these shows have a LOT of effects. When it came time to release ST:TNG on Blu-Ray, they had to recreate the effects and apply them back to the original material, which was a large and costly undertaking. Since it didn't make enough money, they have no plans to do this things like ST:DS9, unfortunately.
Wikipedia has more details about Babylon 5's transfer issues. They shot the show on Super 35mm film so they would have a widescreen source, which they telecined down to 4:3 for broadcasting. But when the show was remastered for widescreen in the 2000s, the production company did not return to the original widescreen film. They converted a 4:3 PAL copy to NTSC and then upscaled that to widescreen!
What do you mean by this? Is it common practice to "remix" a show when it's rebroadcast? I just assumed they more or less press play on a .mp4.