Yes, I think it’s not very clear how the GM uses Fear and that’s somewhat down to trying to split the difference between PbtA rules (“GM makes a Move in reaction to PC moves/results and when it’s appropriate”) and D&D etc rules (“NPC goes when it’s their turn”).
As noted, the GM gets slightly less Fear than players get Hope, on average, but can accumulate more. If the GM doesn’t spend much Fear early on then they can end up blowing all their Fear in the last fight and making the PCs’ lives very difficult, which is what can happen with Trouble/Doom pools in Cortex.
I do like the creative uses of Fear in the Adversary listings, such as Scapegoat for the Courtier (spend Fear to make a major NPC or crowd believe a PC is to blame for something) or Exile for the Petty Noble (spend Fear to exile the PCs from the noble’s territory, giving them Disadvantage to do social stuff there).