So cruising along at FL370 your EAS would constantly change because of flying through different pressure systems or isobars?
Wrong pressure. EAS accounts for the dynamic pressure increase within the pitot tube itself, not for a meteorological pressure system.
The effect isobars create is changes in wind speed, which would affect GS, not EAS. The only way that EAS would be affected by flying into a new pressure area would be if the IAS changed. Now, IAS may change due to temperature changes when flying with reference to a specific Mach number, but saying that EAS changes because of that is akin to putting the cart before the horse.