Tripping a circuit breaker when using a half wave rectifier
Now average RMS current is only 10A even though peak RMS is still 20A


No, it's 14.14 amps and quite close to the breaker's limit.

If the current taken is normally 20 amps RMS for a full AC scenario, you can project this to power by squaring. So 20 amps becomes 400 amps squared. It is the power that is halved by introducing a half wave rectifier so, 400 amps squared becomes 200 amps squared and, the effective RMS current is the square root of 200 i.e. 14.14 amps.