Existing/New Civ design question

So rather than talking about specific bonuses, I want to go full SotL and ask about how many unit types (and how well) a given civ should be able to counter. If we take a look at one of the more funky unit types, high pierce armour infantry (huskarls, champskarls, eagles), some civs have very viable counter units (janissaries, teutonic knights, chu ko nu). Naturally these counter units might have a downside, going teutonic knights against eagles will result in a complete inability for the teuton player to choose the location of any fight, and they are vulnerable to archers. But counters of sorts are available.

The Mayans, whilst being overbearing in the early-game, do not have a viable counter to mass huskarls with plumes doing 2 damage if my math is right and no champions, heavy cavalry, gunpowder, or siege engineers for scorpions.

Against bombard cannons/good onagers, the Chinese lack block printing and so will struggle to convert, lack their own bombard cannons, lack siege engineers for a lucky onager shot, lack particularly good cavalry.

Naturally this is more of an exception than a rule, typically most civs have options to deal with anything, but it got me thinking. When designing a civ, is it necessary to have viable options to counter cavalry, infantry, high pierce armour infantry, archers and siege. Or, is missing one fine?

Finally, how does your response to that question inform your opinion on the current civs?