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Things that are cosmetic, but I'd like to have
-Toggle-able following Pokemon. You can have your entire team out walking with you. Some can even assist without using an HM or being on a Ride Pager. Even then, you can still use a Ride Pager (only without having to wear the gimpsuit)
-Day/Night Cycles and weather varies by location.
-Visible Pokemon encounters. They can appear as the generic "coded" monster designs from Gen 1 to keep whatever encounter it REALLY is a mystery.
-Environmental hazards. Areas that may require you to use certain Pokemon that can adapt to said areas. Fire Pokemon can endure a volcano, Water pokemon can dive, etc., You can still bring Pokemon outside this type but areas may drain their HP or hamper certain moves.
-Friendship system. Think Pokemon-Amie except trust and friendships between your Pokemon. This raises chances of your Pokemon protecting or assisting each other in Triple or Rotation battles (i.e. Buzzwole lifts up Heliolisk to tank Earthquake in its place or Sableye distracts a Prankster from using Spore on Gallade, Victini randomly uplifts a Pokemon to raise a random stat or two -- sometimes drastically.)
-More "weapon" Held items like Thick Club