When clicking with a Steam Controller's emulated mouse the cursor disappears. You can make it reappear if you bring up the Steam Overlay. This happens regardless of if it was launched in BPM or not. Use of a normal mouse does not cause this.
my system: https://gist.github.com/nstgc/02457d7920931a3f8d69cc7b9fa41a2c
Turning off the overlay doesn't help.