The original issue was “Hey, regular TIEs like that don’t have hyperdrive!”
With Vader’s TIE it would be “Hey, Vader didn’t take his TIE to go to the DSII, where did that come from?”
With the shuttle it would be “Oh, I guess the DSII explosion was reeeally overpresented in ROTJ if there’s ships inside that still work!”
And that last one feels better than the original TIE because while you still have to accept that the DSII ‘sank’ more than blew up, at least the ship he used was about as plausible as the TIE but has hyperdrive.
I bet JJ would’ve used Vader’s TIE if even he thought he could get away with it.