Explain that one more time.
How was the dryer's neutral to frame bond carrying all of the neutral current for the whole house when the neutral conductor from the house panel to the service point was compromised to begin with?
Two things had to have happened:
1. The service neutral was broken after the main disconnect, but the EGC was still intact.
2. The dryer neutral and the dryer EGC were mistakenly tied together by the installer.
Thus, the neutral current was flowing from the neutral bus to the dryer neutral, through the above-mentioned connection in the dryer, back on the dryer EGC to the service, where it was bonded to the neutral on the supply side of the neutral break.
It's similar to a broken neutral causing a neighborhood metal water-piping system to carry neutral current to the neighbors' still-intact neutral through everyone's water-pipe bonding. That's largely why the water-pipe GEC is sized for the service.
Had the incorrectly-made connection never happened, the typical lost-neutral imbalance issues would have arisen when the neutral problem first occurred.