Also pressure regulators (like the one on the side of your house) have to vent to bring down the pressure when the network is too high.

No. They have to vent if your household pressure is too high. If, for example, cold gas was admitted into your lines, and that gas heated up, the pressure in your lines would increase. The regulator can’t push that gas back into the high pressure main, so the regulator would have to bleed off the excess pressure.