While there may be some rationality to wanting to see a run through a game without abusing glitches and sequence breaks, the problem with this is one of definition: How do we define what is and isn't a glitch, and how do we define what is and isn't a sequence break?
Let's assume that in some game you could, for example, grab a ladder 1 frame too early because of a programming error, thus allowing you to climb that ladder 1 frame faster than what the programmers intended. This is technically abusing a glitch. However, I doubt any of the glitch-hating people would protest too loudly if this was abused anyways because it only has a minimal effect on the end result.
The problem is: Where do we draw the line? Grabbing a ladder 1 frame too early because of a programming error is acceptable. Skipping the entire level abusing a warp bug is not acceptable. Where do we draw the line?
Maybe "shows the original intended route" could be the line? It, once again, falls down to the definition of "intended route". How much can you deviate from what a first-time player would play before it becomes skipping the "original route"? After all, a first-time player of the game would probably eg. visit all or most rooms which are obvious but not required to pass the level. If there's a room which doesn't need to be visited to pass the level, does it belong to the "original route" or not? Why not?
Another example is if the TAS would skip a normal route inside a room for example with a superhumanly accurate jump, saving something like 200 frames. Does that count as skipping the "original route" or not? Why?
"Visits all all rooms which are part of normal minimal play" would not be a good-enough rule of thumb, because in many games bad glitches can be abused to zip through rooms in 1 second, although it would take something like 30 seconds at least to pass the room by normal play, even when trying to pass it as fast as possible. Abusing such a glitch would probably be categorized as forbidden by the people who want to "see the game".
Of course, if it all comes down to wanting to "see the game", there are many other problems related to that besides glitch abuse. For example, if a boss is defeated so fast that it doesn't have time to switch to its final super-mode, that constitutes, technically speaking, a sequence break, even if no programming error is being abused. It's simply that the programmers didn't expect anyone to be able to beat it so fast. What should be done in this case? Should the TAS deliberately wait for the boss to get to its super-mode before defeating it?
And if you really want to "see the game", wouldn't it be great if you could also see all the types of weapons and other features of the game and its enemies? For example, wouldn't it be nice to see all the attacks the final boss has? What should the TAS do? Deliberately wait for each single attack of the boss to happen before defeating it?
My opinion is: If you want to see the game, play it yourself.
(Edit: Btw, playing the game through first and watching the TAS after that is actually quite rewarding oftentimes. For example, I played Super Metroid through, after which I could appreciate its TASes 10 times more than before. I really recommend it.)
