If your on-call system makes people want to pull their hair out all the time, then you have a problem that you need to fix.
Back when our team was small, we put together a single on-call rotation. Every dev was in the rotation and would go on-call for one week at a time. When we first started the rotation, our team was made up of five devs. Years passed, and despite our team growth, we still stuck with the single rotation. Eventually, the team grew so big that people were going on-call once every three-to-four months. This may seem like a dream come true, but in reality, it was far from it.