I always worried that it was a vampire draw on the battery and made the waste problem of batteries worse. Open to being wrong though

Prairie dogs along the front range of Colorado, deer in the Colorado mountains…

I wouldn’t cap it but put in a Studor vent if there is a chance that you need more venting.

They make what is called a studor vent for this situation. Not sure if there are code restrictions for different areas. If allowed you can put them under sinks etc to get better venting of sewer lines.