They are just there to reduce burning of contacts or EMF spikes blowing solid state switches.
You do have a problem on 3 phase since there is really no "zero crossing". The switch, mechanical or solid state, is opening under a load every time. At IBM we ended up sizing SSRs many times higher than the load would imply, like 45a SSRs on 3/4hp 208 motors.
If the RC was gone, the SSR was on borrowed time. The SSRs failed shorted more often than not. That usually cooked off a motor breaker.
They were tweaking the spec all the time, usually going with higher voltage ratings on the capacitor.