Bearded Dragons are solitary by nature and can even be aggressively territorial when housed with their own kind, they do not get lonely, or have any need for a bearded dragon companion of the opposite gender or in some cases, even the opposite gender will stress them out. Not being able to settle in their own tank will lead to constant stress, negatively affecting their overall well-being. Surprisingly when it comes to humans they do not seem to mind us, which is one of the main reasons that beardies are a very popular reptile pet, because they are so popular there are many bearded dragons needing homes which is why they often get promoted to be sold as pairs when this really should not be the case unless you have separate tanks.
Dragons that have been put into the same tank as another dragon are going to either submit or dominate the other dragon, which leads to stress for both dragons. Big box pet stores do keep dragons together but this is meant to be temporary for the short time that they reside in the store and even then injury and death still occur due to this. They are a devastating example of what can go wrong with missing toes, limbs, tails, or worse in many cases - death. Even though pet stores mean well, they will often try and sell dragons together as not all employees will be versed in why it is a bad idea.
Breeders will need to house dragons together in order to get them to mate and produce young, but this act can often be rough on them as they are not very gentle, and they will often be separated after the act has taken place to allow the female to be able to lay eggs comfortably without the male trying to constantly mate with her. There have even been cases of males mating females to death.