New features:
An open world section of the game, where you can explore randomly generated areas with other players and have the chance to catch rare Pokemon, or maybe Pokemon with unique moves, such as a Pikachu with Surf or Fly for example. Maybe in this you can team up with other players to capture a legendary. I'm thinking take the social aspects from Pokemon Go and make that work with a traditional Pokemon game. This doesn't even have to be in the main story section of the game, however could be an unlocked safari multiplayer type feature post game.
Improving the communication within the game would be nice, this seems to have regressed in Gen 7 to the point where you can't even type your own message when putting a Pokemon on the GTS. We should be able to voice chat in game at this point, that would be essential for the above open world idea.
Retaining more of the information for Pokemon imported from previous generations, for example the date / route it was caught, not just replacing it with something generic based on the game it came from.
Some returning features i'd like:
National Pokedex - as someone who enjoys the collecting aspect of the game the most I really don't like how it's absent from all Gen 7 games.
PSS - I did enjoy having this up as i'm randomly playing the game, it gave the feeling that your playing with other people as you progress though the story.
DexNav - I liked this, from a collecting point of view this was extremely useful.
Wishes:
Don't milk the franchise, by that I mean don't release Gen 8, then release the same game again a year later, slightly changed... (looking at you Ultra Sun and Moon). The Switch is a modern console, an expansion pack released at a later date with new regions to explore might actually work well for a Pokemon game if done right.
Don't go overboard with all the cut scenes, I felt this was too much in the Gen 7 games.