The above is true, Draeni were using just the human paladin horse until Wrath, and Dwarves the same until Legion/BFA. They could simply do the same giving them the stock human/elf horse until they later get their own racial mount.
Or do something like was speculated in another thread and do like they did with DK’s, and have the new wave of Paladins have a theme (such as the resurgence of the Silver Hand in legion) and give them a new shared Paladin mount from that, until they get their own unique racial ones later.
That way people can be the paladin race they want to be sooner, and get the racial mount later.
Warhammer 40,000 already did it, so Blizzard could just borrow from them like they borrow from virtually every other franchise:
From the weakness of the mind, Omnissiah save us.
From the lies of the Antipath, circuit preserve us.
From the rage of the Beast, iron protect us.
From the temptations of the Flesh, silica cleanse us.
From the ravages of the Destroyer, anima shield us.
From this rotting cage of biomatter, Machine God set us free.
– Chants of the Journeyman Verse III