I'd take a long hard look at the effect and see if it made any sense for that effect to do anything relevant to a creature in flight, probably case by case e.g. something that affects a giant owl's flight might be ignored by a dragon or roc or nearly destroy a normal bird.
They generally involve a Str save, which should handle that for you.
My quibble is that the way the rule is written, the creature so affected is given no chance of regaining control of its flight before hitting the ground. It's as if the writers assume all aerial combat will take place within a few tens of feet of the ground
A combat round is six seconds. When falling, one's acceleration is (to first approximation) 32ft/s^2. Starting in level flight, in six seconds of falling, then, one drops 576 feet. So, they are assuming it is within a few hundred, not a few tens, of feet from the ground.
The solution to that is to simply continue the analogy. If it takes more than the time to the creature's turn to hit the ground, the creature takes half their movement to regain control - like a creature uses half their movement to rise from prone.
When I read "has its speed reduced to 0" I don't immediately leap to thinking of that as permanent immobility
There's stuff that'll reduce your speed to zero temporarily. Being Grappled or Restrained will reduce your speed to 0, for example, and those are conditions you can remove - they aren't necessarily permanent.
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