Camels might become more popular anywhere that is fairly dry, but IIRC, they don't do so well where it is wet and cold. Plus, their wild ancestors were kinda limited in availability. Oxen were used early on for pulling and plowing; riding them would be the next step. They might not be fast as horses, but without horses, people wouldn't know that...
Camelids were wide spread. Dromedaries are but one variety of surviving camelid and have "niched" themselves into the hot arid desert environment, but they are not necessarily locked in. Don't forget Bactrian Camels, which spend their entire lives in cold. And of course the entire Llama family was much more widespread back then and far more diverse. These are all running animals. The point about defensive strategies of different species is well taken. Horses, camels, llamas are all running animals, more inclined to flight than fight. Cattle are more inclined to gather together when threatened and present a monolithic wall of cranky bovine muscle and horn to any threat. Great beasts of burden, but not suited for Cavalry.
Is the need to actually ride the animal necessary? I'm not so sure. Cattle give me the impression that they tolerate a person on their back (I'm thinking the water buffalo in the rice paddy being ridden by a young boy) but they don't seem to be capable, or inclined, to form a bond with humans as horses can. Not sure that camelids can either. I think as beast of burden and haulers of wagons, carts, wains and coaches cattle may be well suited, if slow.
I think that if humanity is deprived of horses that we would utilize multiple species for different tasks. We did that any way, but I believe it would be deeper. Cattle for drayage, plowing and assorted heavy tasks (in some areas and for some tasks this would be elephants, camels, reindeer, etc.) Camelids for fast transport and warfare (some of the ancestral llamas were built to be extremely agile. I do not think we would be employing deer or their relatives too much for riding because their gait seems to be unsuitable but they would be utilized possibly for carriages and sleighs...nothing new there.
Lat word about llamas, had early llamas been domesticated they could have been selectively bred for strength, speed, size etc, and under man's protection these larger varieties such as the large headed llama found in Florida may not have gone extinct. Needless to say, I think the best horse analogues are the camelids.