All of this has to be created again, and that would in no way be the original show anymore.
Well yes, that's self-evident. It was designed to be seen on a small 525 line CRT television in very much standard definition.
Any attempts to make it available in HD will mean it is no longer the "original" version. However, does this actually matter? Are you damaging the original creative intent by rescanning it all in high definition, and very probably altering the visual effects?
I would argue that the important thing is that the story and the creative intent remains the same. As long as the episodes are edited in the same way, and have effects which help to tell that story, it doesn't matter if someone has had to redraw a 1989 phaser blast on a computer in 2009.
Does it make it a "different" show? Technically, yes, but to all intents and purposes, of course not.