My answer is yes, the on-call compensation is more about keeping healthy dynamics of on-call than it is about materially impacting your total comp.
I've worked in places where on-call pay was material before, and while it's nice, it comes with disadvantages too. As an example, you try hard to keep shifts balanced because if someone covers you and you don't do a shift that month, you notice it in your paycheck.
That's not always a good thing, if you want to encourage people to switch shifts to prioritise their health and reliable on-call cover.
I would never accept on-call work (even if paid), even if no incidents ever happened because of the infringement that has on your lifestyle. Realistically it means I won't be able to attend church the Sundays I'm on, go for a long run, on a hike (if we have one of the only nice Saturdays of the year), or even visit family (some of my family have a terrible internet connection!), because even if nothing happens then there's the risk something _might_ happen: and if it did, I wouldn't be able to respond if I were doing one of those activities. And for me, no amount of money would be enough to compensate me for that.
I take your point though, and if being on-call is having any meaningful impact on the time you spend working outside of hours, I agree $350 is low. For us, we're an early-stage startup with low numbers of alerts (long may it stay that way!) and the impact is low.
Not to try and defend it too much, but it's worth pointing out that the $350 is there to cover the inconvenience of being 30 mins from a laptop, rather than compensating for the time. We also give folks time off in lieu for any time they spend working outside of hours.