The final sentence of the Haste spell reads:
When the spell ends, the target can't move or take Actions until after its next turn, as a wave of lethargy sweeps over it. (PBH p. 250)
If a creature such as a wyvern, pegasus, griffon, etc. is flying while hasted (that is, under the affect of the Haste spell), does it fall when the Haste spell ends since at that point the affected creature "can't move"?
A cursory reading of the paragraph under Flying Movement in the PHB seems to suggest that it would fall:
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, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell. (PHB p. 191)
But I'm not confident that I haven't missed some subtle nuance in the wording of the rules that would argue otherwise.
The Sage Advice Compendium 2019 has this paragraph:
Can a flying creature without the hover trait stay in one place while airborne, or does it need to move each round? A flyer that lacks the hover trait can stay aloft without moving each round.
The language in the Haste spell description does not impose any formal conditions (such as Incapacitated, Stunned, or Restrained), nor does it state that the creature's speed is reduced to 0 feet. So I am wondering if the words "can't move" in this context are sufficient to establish that a creature in flight must immediately begin to fall (as a wave of lethargy sweeps over it) or whether there are reasonable grounds to argue that according to RAW or RAI it can remain aloft without "moving".
Best Answer
Your interpretation is correct
When the haste spell ends, the target cannot move. This counts as being "otherwise deprived of the ability to move" for the sake of remaining aloft. The creature would therefore begin to fall unless it has the ability to hover.
I researched this part of the rules when writing this related answer and there are no "subtle nuance[s]" or hidden rules. Remember that spells only do what they say they do and there are no hidden rules. If the rules for haste intended to give you some protection against falling it would say so.