I think it’s meant to be more of an overall vision triggered by tapping into the dark side, similar to what Rey experiences first, the words we hear from Palpatine are what he already said before. And at least in this version Rey’s vision can’t be coming from Palpatine, since he wants Rey dead for real to “end the Jedi”, it doesn’t make sense that he would be stoking the flames of her inner darkness.

Moreover, I think the main purpose of the visions, specially in splitting them up, is to set up each character’s motivations and their journey throughout the film. And as I said before, changes have been made so that the Sith throne is only relevant to Rey’s journey. I guess you could rationalize the vision as Kylo rejecting the throne as he refuses to kill Rey, but I think it’s better to just outright remove any indication that Kylo would need or even want to overtake Palpatine’s position, when he just spent the entire last movie struggling to overtake the position of Supreme Leader.