In 1v1 I think its hard to justify the investment. For TG, its niche-y, but I can think in three situations:
a) when there’s trade, if one can have two sneak Archery Ranges close enough to the opponent’s trade line to be there fast, but not close enought to be spotted, Cuman player would be able to have 8 HCA by the time any of the other civs would have 4 (carts die in 7 shots, IIRC);
b) your team need from time to time a quick answer to halbs killing your allies cavalry;
c) your team is a push-forward-pushed-back situation and even if you all could have dozens and dozens of buildings to keep training army, a HCA that trains in half the time would be better than +1 range/attack to keep your numbers up faster than your opponents.
Not the best examples in the world, but I tried 
Fair shout to be sure. Never would have considered DM had you not brought it up, so you certainly scored your point already. 
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Oh just saw OP’s explanation as well.
Still don’t agree that Cuman CAs are beyond average - I would prefer a generic CA most of the time as you prob spend more than 5% of that movement speed shooting something that you can kill already with that +1/+1 attack AND range (which is the real killer).
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