I don't think horsemen are fine because they are bad against their +era counter (which they are). I think they are fine because they really aren't any more powerful than going for early swords or, ffs, BC rifles. In fact they are a lot weaker than BC rifles. In other words, I think horsemen are not quite as good as their contemporary, swordsmen. They are a little easier, a little more plentiful, but ultimately the weaker choice, I think, if you have to clear out a Pangaea on high difficulty and a standard or harder map.
I understand and can appreciate your statement that a rifle rush may be superior to the horse/knight track long term. But your statement that horsemen are worse than swordsmen as contemporaries is way over the top and not supported by the facts.
-Horsemen take less tech investment to research 208 beakers to get to HBR vs 253 to get iron working
-horses appear at animal husbandry 38 beakers into the tech path. Iron doesn't appear until the full 253 beakers are done. If you don't have iron then, you are in deep trouble. If horses don't appear after those 38 beakers (which I've yet to have happen to me over many games), you can go the sword path and only be a bit behind where you'd be otherwise. Taking into account research rates and the time needed to either mine the iron or move a settler to settle on iron, swordsmen come out about a dozen turns after horsemen.
-horses are more plentiful than iron on the maps
-horsemen have more strength 12 vs. 11
-horsemen have more move points 4 vs 2
-horsemen can move after attack, swordsmen can't
-horsemen can take a city and retreat out - important for those scenarios where the ai retakes the next turn. With swordsmen, you lose the unit with the city recapture
-horsemen move so much faster, they can get to and participate in many more early battles, earning XP faster than swordsmen
-horsemen can take units in open terrain and retreat out, swordsmen get stuck in the killing fields and die.
-the horse tech path gives better early benefits than the sword tech path. With horses you get pasture building for some food (and production with horses), roads for gold and circus for happy in those 3 techs. With swordsmen you get mining (which is good if you have gems, gold or silver nearby but otherwise not so useful in the early game with only a few pop points), and some military buildings.
On the plus side for swordsmen:
-horsemen have a designed counter with spears and pikes, swords don't
-swords get rough terrain bonuses, horsemen don't. Note that about 80-90% of standard maps are open terrain, so if you need to avoid fighting on rough terrain, you usually can.
-swords have a quicker tech path to upgrade than horsemen.
The biggest benefit to horsemen is that horsemen get out a dozen turns sooner, and can make it to their target another few turns quicker than swords, which means you'll conquer your first civ city much much earlier with horses, which will translate into more production, gold and beakers down the road. A quick start snowballs, and horses are way quicker out the gate than swordsmen.
Bottom line for me is that horsemen blow the doors off swords. They are faster to tech and produce, more consistent to have the resources for, get to battles quicker, are stronger and faster and have more survivability.
Oh, and Swordsmen do have a hard counter. It's called "horsemen".