Emphatically Deezer for taking a very Deezer centric view and thinking that users just want a remote control feature for another instance of the Deezer app, as opposed to a proper casting mechanism as developed by Spotify, Tidal, Amazon Music and hopefully very soon, Qobuz.
The WiiM devices are based on a Linux variant (Tina I believe) and can’t run mobile apps such as the official Deezer app, so have to rely on the third party API provided again by Deezer which as you’ve discovered isn’t as feature rich as the native Deezer app.
Re stuttering in the WiiM Home app, have you tried rebooting your WiiM device and/or router? If the issue persists, the route to a solution is to submit a ticket to WiiM from the settings/feedback section in the WiiM Home app so they can inspect your device log for evidence of the issue.