For a unit that is too vulnerable to conversion and ranged units, the War Elephant is too situational to be of any use. Might as well set the Sogdian Cataphract as the main unique unit for the Persians.
And as for Franks, the Frankish Paladin (currently hero) would be better suited as the Frankish main UU, because there are two problems with the axemen: 1) sluggish firing rate and 2) seems out of place as they are obsolete by the time of campaigns set in the 11th century onwards (Joan of Arc, Grand Dukes etc).
I basically see no need to change the Unique Units for Persians and Franks. Even without War elephant, Persians are strong in cavalry and although the war elephant has many disadvantages (slow speed+high cost) yet it has some strong attributes too. In Late game, when resources are too much, a persian player can hurt its enemies alot with Elephant as they can destroy buildings (Castles easily) and many melee units while persian wood-costing Crossbowman, cheap and fast Hussars and other units tackle enemy’s anti-cavalry units and monks. And yes, its very situational but still not an exception as many other Unique units are too like Jaguar warriors, Arambai etc. However, i do think that the last Unique tech: Mahouts, should make them 30% faster and cost -40% resources. War elephant are basically unstoppable units if played rightly and on good condition. In Late team games, i have won a lot of game with this Unique unit. So i think, persians deserve such a tank.
And i think that same goes for Frankish Unique unit too. They are situational too but Frankish Paladin don’t need their help most of time.
Yeah, I do think that Frankish paladin should be a UU that you can upgrade from cavalier like Winged hussar. But they need to nerf hp stat of the current Frankish paladin a bit because they will have 210hp in total with Frank bonus. My proposal would be nerfing their hp to the same generic paladin, keep their +1 attack and give them +1 range (because of the long lance)
Throwing axeman is fine. It’s not that we really lack anachronistic UUs (huskarl vs janissary, for example).
The Persian “war elephant” is okay if we’re in AoK or AoC, but now we have ~10 civs that have 3 different shared elephant units, all with specific purposes. “War elephant” now sounds, looks and functions too generic to be a UU, not to mention it was not iconic for Persians.
It’s like all European civs get a few unique knight variants in their stables like chevalier, templar, gendarme, etc. and one civ gets “knight” as a UU from its castle.