To be fair, they do often allow for doing new things after the game, however limited. It is true that these often don't acknowledge your being such or seem to, but anyway. G/S was a bit strange with this, with you basically taking on the Kanto gyms just so that some guy will give you access to Mt. Silver on doing that, or in brief as a means of grinding, which fortunately wasn't that significant because at that point the plot did recede in any situation. It's perhaps problematic, though, because if you're Champion, but presumably can't lose this - and it is the end of the game on some level, so you wouldn't necessarily want them to un-end the game, as it were - then that might not mean much in most cases and could get iffy. In addition, they might not want to leave the end of the game completely up to players. In addition, this might mean that things get too difficult or easy because of hacked Pokémon, etc. One option might be that the Champion obtains a Pokémon or so each time they are defeated, in other games, from the player who beat them - while they retain this, of course - with their team having some amount, say 4, of these rotating, and this updating each time the player is connected, unless that took a while. However, this could be an issue for the moment, and in any case still seems to be leaving the end-game up to a bit of a mixture of opponents, so it would generally work mostly if they didn't want to make any particular statement with this trainer. In any case, leaving the whole end-game up to one random, hopefully legitimate player, might be something they're reluctant to do.
At the same time, most such approaches would leave things open to hacked creatures, possibly low-level ones or HM Slaves, etc., appearing there, which may give a strange impression or distort. Certainly, though, actually playing for the player without them being there, and making their situation contingent upon this, seems like it might be going a bit far. In addition, having the player face themselves as Champion seems most likely to be humorous, and it wouldn't make sense for this Champion winning to somehow default the position to the original. At present, given indefinite Champion status, or that that is the end-game, the usual mode is probably preferable, although to be fair you wonder if the position itself isn't a bit unnecessary, as it began as a twist in the first game and has by now stagnated pointlessly into a position which is just taken for granted or left in there. It may be strange for some people that it's taken for granted that after beating the Elite 4 some recurring character the game likes shows up and has to be faced as well, so you wonder if that kind of thing might be based on assuming that the fanbase is just people who liked previous games, and probably reducing. In any case, we'll see if they have any plans for that, but for S&M they probably want to say something or other with that NPC, so it might seem reasonable to keep that character in to allow for their role as a possible throwback, etc., if the role is retained in their plans. Honestly, they could just throw in a Charizard in there, or a poem by Campion or Marx to end it in the mode of The Void, it would be an interesting twist on a by-now stale position.
