This is correct.

But there is a bit more. Almost all power plants in Pakistan are built with state-backed dollar-denominated loans (reason govt incompetence+corruption). This means if grid demand goes down, power plants don't go out of business like they would in a market based system. Instead, they keep collecting dollar-denominated interest paid by the state, even if they produce zero power.

The state mitigates this by increasing electricity prices (in rupees). I have forgotten how this helps.

Don't they charge a minimum just for keeping the wires connected?

its easily fixable, utility company can charge fee for fixed cost those who connected to the grid, and if all rich decided to disconnect, then they disconnect neighborhood eliminating fixed cost.