I come from a more mechanics-based angle in that I consider passive damage to be a fundamental concept and thus a mon should have access to it unless they have a gimmick movepool preventing it. The replacement wouldn't need to be Poison type.
(also, Poison Powder is exclusively learned by Grass and Bug types, the only Poison types that learn it are Grass/Poison or Bug/Poison)
There are 292093232 forms of passive damage outside of status. Most Mons have some passive damage, even if its temporary:
Grass: Leech Seed, all kind of powders.
Fire: WoW, Fire Spin, Magma Storm.
Water: Well, Scald and Whirlpool.
Bug: Infestation. Some also learn Toxic or Poison.
Normal: Wrap. Normal Mons tend to have either a large movepool or a secondary typing that gives them some form of passive damage.
Poison: Welp, you know about this one.
Ground: Sand Tomb and a big one, Spikes (currently learnable by a very big percentage of Ground Mons).
Fight: Well, nothing here, apart from secondary typings (Breloom gets Leech Seed, Toxicroak gets Toxic). But its the most offensive type, so its fine.
Psychic: Nothing here either. Most do have secondary typings.
Rock: Stealth Rock is a big one. Sandstorm and Salt Cure exist too.
Ghost: Curse.
Ice: Hail used to be this, but not anymore. Freeze is way better than any passive damage though.
Dragon: Nothing here. Dragon Tail + hazard does bring some passive damage, however.
Steel: They really should have made the Copperajah Gmax Move into a regular move with limited distribution.
Dark: Ceaseless Edge, though only one Mon has it. There is Flatter for confusion, I guess.
Flying: Not exactly passive, but confusion from Hurricane and Chatter. Beak Blast brings burn if you touch Toucannon.
Fairy: Nothing here except some confusion moves (Sweet Kiss and Strange Steam).