It's not as simplistic as you're making it seem.
I've been fuming about Crossbows for going on eight years. You will lose this debate, because I've considered the issue from all angles.
First of all, Crossbows are stealthy while AR bullets are not.
This is the perennial justification for Crossbows' inferiority, but the problem is that Crossbows aren't good enough at killing quietly to justify their incredible disadvantages. The bolts around which the weapon is actually balanced—the ones that pop, fizz, and zap—are not quiet. Regular bolts and special bolts that are silent are a joke compared to the damage output of, say, a silenced Spec Ops SMG, a gunslinger's pistol, various silent and 100% accurate psi combinations, et cetera, not to mention sniper rifles, which can actually kill four or five enemies in one go using no special crafting components whatsoever, even though they don't do so quietly.
If five bodies fall in a room, and no one is around to hear the shots, have I achieved stealth? We don't need the Ferryman to figure that one out.
Second of all, Crossbow bolts can be outfitted with multiple different types of utility so that you can deal with a large variety of situations and enemy types. Third of all, Crossbow bolts operate at a different velocity and are not subject to ballistic plate bullet penalties, which is very important when dealing with energy shields and different types of armor.
In one breath, you describe the fact that Crossbows can be fired stealthily; in the next, you describe all the whiz, bang, pop, and fizz they're capable of. This is because, unless there is only one or at most two enemies present, noisy hostilities will inevitably commence when relying on Crossbows. You know it, I know it, we all know it.
Ballistic plate penalties are largely irrelevant when employing W2C ammo against enemies' mediocre armor statistics, even after the nerf. My 5mm Expertise Jaguar could obliterate a tin can in one burst while attracting absolutely zero of his pals from the next room over. Also, crossbow bolts incur mechanical resistance maluses at all times, almost like reverse hollow points. And that is their biggest weakness: Crossbows are absolute garbage versus heavy armor.
Nor am I impressed by impact speed energy shield penetration, because when using a non-gimped stealth or ambush weapon to attack enemies, they usually don't even get a chance to turn the shield on; and if they do, I'll EMP them. Of course, when using Crossbows, you might not have an EMP grenade available, because your slots will occupied by all the noisy bolts you'll inevitably have to use in the non-stealthy pitched battle that will follow the subpar ambush burst capability of Crossbows.
All three of these things are benefits the Crossbow has over the AR, and they aren't insignificant. They are archetype and scenario defining differences that provides a ton of RP and dungeon design potential to the game.
One of the side benefits to specializing in a weapon type from the Guns category is that all of the many other types of Guns-related weapons are available to you, including chemical and energy pistols, albeit unspecialized or partially synergized/specialized. With Crossbows, you spend the same amount of skill points and have access to... Crossbows. My endgame sniper is able to erase sea serpents with a sidearm AR or shotgun with absolutely no additional feats whatsoever.
The issue with Crossbows is that they're mediocre in every way, and have a very significant weakness (heavy armor) shared by very few other entire weapon skill categories. Their vaunted utility and versatility come at the cost of crossbows being the only weapon archetype for the Crossbows skill, as well as special bolts hogging utility slots and eating feats like candy. Crossbows excel at nothing. They can't run the table on a field of enemies like a sniper rifle can, they can't systematically and silently burst down a tight group of enemies in a small room like an SMG can, they can't rake an entire enemy platoon like an AR can, and the special bolts are arguably not as strong as top-tier grenades despite hogging the utility slots—let alone psi powers.
Add to this that poisons and bleed are the only other real avenue beyond pop and fizz bolts, in this game where your body count often needs to be at least one per turn... yikes.
A crossbow is basically a gimped (far less damage and range, no Shooting Spree) sniper rifle, justified by the fact that it's quiet, combined with a gimped hybridization of psi powers and grenades tacked on, justified by... the fact that they'd be totally unusuable without them, I suppose.
