The fact that none of the Galarian legendary birds get Heat Wave makes no sense, as Pokemon like Xatu (who has the same typing as Galarian Articuno) and Mandibuzz (who is Dark/Flying like Galarian Moltres) get the move.
As most flying types with wings get the move did I expect the Galarian birds to get heat wave? yes definitely. Most of the birds that don't get it are normally are due to it typing (like how Kantonian Articuno can't get it because its an ice type).
That being said there is a fire type move I think could also make sense for thematic reasons. Burning Jealousy. Particularly Galarian Moltres is the Malevolent Pokemon and the move is known by a lot of dark types (mostly those with slightly darker personalities like Alolan Persian) . Galarian Articuno is the cruel pokemon and is said to be callous which I feel for thematic reasons feels like it would make sense as while its not a dark type it does suit the personality. Galarian Zapdos is the least of a direct connection but it was described as being a belligerent, battle-hungry Pokémon seems unable to resist challenging Pokémon it senses may be stronger than itself which could sort of fits the motif for the sort of pokemon that get this move but I admit the reasoning is less direct that the other two.
Galarian Articuno getting not Heat Wave I can understand. I can sort of see why Galarian Moltres doesn’t get it as well. Galarian Moltres doesn’t actually have fiery wings like it appears to have. It is the result of some sort of dark energy that fuels Moltres’ rage. The “fire” is basically an aura that Moltres is giving off. Galarian Zapdos I could imagine being able to use Heat Wave by simply running around its opponents in a circular motion extremely fast and the friction creates some sort of heated vacuum that closes in on to the targets.
Of the 3 I'd say Galarian zapdos is the one i'd least expect to get it as it has atrophied wings whereas the other two have fully formed wings which is for the most part required for flying types who get this move. Still I'd give it to all 3.