It makes it more dangerous : the sting is attach to the venom bag, so the venom bag gets to empty itself whole if it stays. Evolution would have chosen the survival of the hive, not the survival of the bee.
One thing is weird though : you can extract the sting of a wasp with a pincer. The wasp will live through it. Why do the bee dies when it loses it’s sting and not the wasp?
Horse archers, or skirmishing units in general, are countered by archers or siege units. Unless the game is wildly unbalanced it always works.