Yes, I've installed Komplete Kontrol and it works in the app. I can also use Komplete Kontrol instruments inside Logic with the keyboard.
When I go New > Scan All Models the only Native Instruments controller to show up is the Komplete Kontrol S61. I've also tried deleting the Logic files in Library > Preferences.
The transport controls work in Ableton too. Perhaps you're right about NI needing to fix it, although I have heard that it works for some people in Big Sur with an M1.