The reason is because you no longer have lifesteal because you are no longer Frost Lich Jaina.
The same goes if: You play Mage and you cast Frost Lich Jaina to transform. Later you play any other hero. Now all your elementals will no longer have lifesteal because you are no longer Jaina DK.
"Unlike Lord Jaraxxus, although Ragnaros minion is an Elemental, Ragnaros hero does not count as an Elemental. Frost Lich Jaina's battlecry cannot give Ragnaros hero Lifesteal, which means damage dealt by attacking an enemy or using hero power does not restore health to hero."
F..k inconsistency, although this could be just an oversight from Blizzard as OP suggested.
This is also on the Hearthstone Wiki:
https://hearthstone.gamepedia.com/Majordomo_Executus
"Unlike Lord Jaraxxus, although Ragnaros minion is an Elemental, Ragnaros hero does not count as an Elemental. Frost Lich Jaina's battlecry cannot give Ragnaros hero Lifesteal, which means damage dealt by attacking an enemy or using hero power does not restore health to hero."
F..k inconsistency, although this could be just an oversight from Blizzard as OP suggested.