No, it doesn’t just go to heat. It is much worse than that.
Without the grid’s resistance, all generators start spinning faster. That drives the AC frequency up – which also make all big industrial motors to spin faster, as they are synchronized to the grid.
Raising generator speed also raises voltage (“electrical pressure”) which, if raised unchecked, can burn all electrical equipment on the grid.
That’s why it is very important to match consumption and production. Fortunately, the AC grid “automagically” equally distributes the rotation speed between all generators and motors, and because their total mass is quite big – it gives a bit of delay before any critical spinning up happens.
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