I like the simplicity of the rules as they are currently written. However, I do think that you can probably use a house rule that allows them to move+shoot as long as they spent the turn prior completely immobile (no move, shoot, fire, spell, etc.).
It won't be a major balance issue but will tip the scales slightly in favor of the XBows. It really does make a big difference if they can hide out of range or under cover and "prep" their weapon, then rush forward and use it the next turn. That free turn of shooting isn't something to be taken lightly. It may only be a minor thing but without several games of testing you never know.
From a reality perspective, walking around with a loaded XBow probably was not that easy of a task. I would imagine doing so might have been prone to misfires, especially if you tried to run.
Even a modern XBow or firearm (rifle, pistol) isn't something I'd rush around with fully cocked back and ready to fire on a hair trigger, and that's with modern precision manufacturing.
I think XBows work well if you keep their limitation in mind in your strategy. If you have any valuable objectives near your starting zone, use them to cover it. If you have to advance, advance them at full speed with the rest of your force then let them set up to provide cover fire. In most games we play they are able to get to a good flanking position either during the Move of Turn 1 or 2 so that by 3 they are shooting. Spread them out a little and minimize the risk of volley fire (and their armor is usually enough to minimize volley risk any way), etc.