How would deoxys work
Answers
Normal is already a glass cannon. That 345 value would be normal form's attack stat. Attack form would have an attack stat of 414 using the stat conversion formula. To counterbalance this, its defenses likely won't clear triple digits.
Defense form would have high defense, making it a trophy and not much else due to defensive legendaries/mythicals not having a place in PoGo at the moment.
Speed form gets a respectable attack of ~230 and has okay defense stats. Being saddled with 100 base HP though means it likely won't oust Espeon or Alakazam in psychic lineups.
All forms only have a base HP of 100. Without high DPS fast moves and quick multi-bar charge moves Deoxys as a whole likely won't oust Mewtwo as best psychic type, even with A-Deoxys having an astronomical attack stat.
Deoxys is a mythical pokemon, so that suggests maybe special research. I think it could be more interesting as a raid boss though. Each form could have a different chance of appearing as a boss, probably the easier forms being rarer. The form you fight against would be the form that you get a chance to catch.
Trading for a form that you have not unlocked would of course count as a new pokedex entry and cost more. After you have unlocked two or more forms, you could spend Deoxys candy (like evolving) to selectively change a Deoxys to one of the other forms you have already unlocked.
Different forms could have different available moves when catching and using TMs, but when you change the form it should retain whatever moves it already has allowing you to use TMs to mix movesets from different forms.