That was kinda my thought process as well. Easier to manage from Discord's side and easy to intergrade on MS/Sony's side.Wouldn't be surprised if it's more on Discord's side. I imagine Microsoft would have no issue with Discord wanting to develop and support a dedicated app for this. Wouldn't be surprised if Discord made this setup for both consoles (PS5/XBS) and it'll be simple enough to hook up to for Microsoft/Sony.
Now the question is if PS5 will support screen sharing.
Guess we should wait until Sony's inevitable PS5/Discord integration though.