I don’t think they care about this feature. Presumably, they don’t see enough people using it to justify properly maintaining it, much less improving it.
As others have said, Moonlight + Sunshine works much better. Add Moonlight as a non-Steam game on your Deck and set it to launch Big Picture directly on your host. That’s my setup and it’s pretty seamless. Ever since the Big Picture update for the desktop client, I forget I’m even streaming sometimes because the interface is the same.
To add to this, there's also a decky plugin called MoonDeck which, once set up, allows you to launch a stream for any game from the game itself rather than from the moonlight client. Really useful if you're someone that likes to customize your controller configuration for each game.
Is there still an advantage to doing it this way after the desktop Big Picture update? Is it different than using the controller configuration menu on the host PC?
If you just launch steam big picture through moonlight and use the host client's steam configuration you'd just be configuring an emulated Xbox controller. (which might be fine for your use case) you'd lose out on all the steam deck specific bells and whistles. No grip buttons or touch pads. If you use moondeck you keep all of the steam decks funtionaitly.
Oh cool, I didn’t realize that was possible. That would be a great reason to use the plugin. I never really play non controller supported games with the Deck, so I just have the track pads set to mouse and scroll for the occasional desktop task on the host and the paddles set to Moonlight shortcuts.