cant use great exalt with homogenizing exalt and omen of greater exalt

As the title said can somebody explain why i cant use great exalt with omen homogenizing exalt and omen greater exalt?

I assume it can't generate a matching modifier.

Homogenizing omens function using crafting tags for modifiers--though I don't think there's a way to view them in-game in PoE2. The ES modifier has the Defences tag, and the Fire Res modifier has the Fire/Elemental/Resistance tags. The increased item rarity modifier doesn't have any tags, so something like an Homogenizing omen will ignore it.

Looking up the modifiers that can roll on Int boots, the Fire Res and Increased Item Rarity are suffixes, and I assume the Desecrated modifier is a suffix as well. So, with an Omen of Greater Exaltation, you're generating two Prefix modifiers.

There are no Elemental, Fire, or Resistance prefix tags. There are only two prefixes with the Defences tag--for whatever reason, the hybrid "% increased ES/+ stun threshold" modifier doesn't have the Defences tag.

As a result, there's only one modifier that the Homogenized Exaltation can add--flat ES.