What alternate unique units would you like to see? This is purely a hypothetical discussion of what if the unique units were replaced with something else at the very beginning. However, you can have some civs with 2 unique units if you wish, such as the Vikings.
Celt’s castle unit. Scottish Nobel Pikeman. A super-heavy infantry very high armor, 100 hp (elite), plus one range, but slow movement rate. Think of it as a cross between a kamayuk and a teutonic knight.
Gallowglass for the celts.
Landsknechte for teutons.
Venition gally for italians,alongside the current uus.
Varangians for byzantines with cats.
Cuman for magyars.maybe as the 3rd upgrade to the cav archer.
Spanish genitor not the berber looking one an european one.
Maybe Sohei for Japanese (warrior monk who typically fights with a Naginata), for the vikings maybe shield maidens (female warriors) and for the khmer maybe some type of guard (don’t know their exact name) on horseback that fights with a ph’kak (like a hockey club but with an axe blade)(their horses could have been disguised as dragons)
Koreans - Hwacha (but they already have 2 uus)
Chinese - Flamethrower
Persian - Savar
Turks - Sipahi?
Japanese - Mounted Samurai (as a cav archer) or Ashigarus
Mongols - some type of unique siege unit would be great, maybe grenadier?
Vietnamese - some type of troop armed with handgonne, not sure how it was called but according to Ming records the Annamese had handgonnes that could fire large darts
Vikings - would like to see a double-handed axeman for them
For me, the Spanish need a signature unit that isn’t a gunpowder one. Missionaries are underwhelming, and just like Conquistadores, they’re thought for XVI century Imperial Spain, in the context of the conquest of Mexico. Spain’s history is more than that, and the Conquistador feels so out of place in El Cid’s campaign