dnd 5e – How does grappling work in the air, when both combatants are high enough?

What happens when a flying high creature is grappled? The rules for grappling state

you subject the target to the grappled condition

and the grappled condition is described as

  • A grappled creature’s speed becomes 0, and it can’t benefit from any bonus to its speed.
  • The condition ends if the grappler is incapacitated (see the condition).
  • The condition also ends if an effect removes the grappled creature from the reach of the grappler or grappling effect, such as when a creature is hurled away by the thunderwave spell.

Keep in mind the grappler hasn’t moved, so it isn’t carrying the grapplee yet:

When you move, you can drag or carry the grapplee with you

The rules for flying declare the creature falls in this case

If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls

(emphasis mine)

Basically the rules say:

  1. the grappled creature’s speed becomes zero
  2. the grappler isn’t carrying it yet
  3. the creature falls, because its speed is reduced to zero
  4. now it’s out the grappler’s reach and is no longer grappled

This sounds like a nonsense for me, so how exactly grappling works for flying targets?

For clarity let’s say the creature flies by non-magical means, using its own wings (a bird, an Aarakocra or something like that), and the grappler can be airborne using any means (magic, being carried by a flying mount, staying on a catwalk, et cetera).

Flying creatures are common in worlds of D&D, so the situation has to be quite trivial. The question is primarily about rules as written, not about adjudicating the situation using common sense.