Arcing does not create an imbalance. But again, is it a GFCI or an AFCI? AFCI would assume arcing is a failed extension cord - cut off power.
Semiconductor switching would eliminate arcing using techniques such as switching on zero crossing (so as to not create excessive heat). Also necessary are numbers for that heater and for switch rating. Switches that cut off more than 1 amp will arc. But a switch is designed to minimize that arc and to not cause contact damage. Snubbing will not eliminate the arc - but will significantly reduce destructive effects.
If a GFCI trips simultaneously with arcing, then current is going somewhere else - where it should not be going. GFCI would be tripping as designed; reporting a potential human safety issue.
Line filters are expensive? What is expensive - a number required?
https://www.google.com/url?sa=t&rct=...68rtmX327KQOjg