Yes.
The designers, in their finite wisdom, decided to tell you "you're playing the game wrong".
"Instead of using two cool hand crossbows, you can and should use only one hand crossbow instead."
Their decision was both wise and necessary. How can you load a crossbow without a free hand? Unless it's fully automatic. You're free as a DM to create such a "load free" variant, but you can't play with the default crossbow and fire with it every round with anything in your other hand, a fork, a knife, a spoon, another crossbow.
Humanoid PCs have two arms, and two hands. This ruling is just common sense. Make up a fully automatic hand crossbow for your game, then dual wield those. Nobody's stopping you.
But if you are letting halflings use greatswords, or anyone ignore the loading property, then no, you are in fact playing the game not by the rules, which is by definition, "wrong" in some sense. It's not a big deal, either way, but I do think not playing by the basic rules is playing the game wrong. And that applies to every game, D&D or not.
You can call them your house rules, which then makes them valid again. But in their wisdom, they decided that fully automatic weapons didn't belong in basic D&D in the default setting. You're free to play with firearms, plasma rifles, blasters, reloading crossbows, anything you want. You just aren't free to use those in the default D&D and expect the rules to follow. Sometimes rules have to be strict, to avoid absurd things like shooting weapons that have bolts but no way to imagine how those bolts are getting loaded.
They did the right thing. In this case, your fun (dual wielding non-automatic crossbows and firing each round) is not more important than mine, which requires a free hand to imagine how those bolts are loaded into the weapon in order to be fired. They sided with rules that make sense, for which they should be congratulated and not denigrated.
Verisimilitude matters, and is one of the reasons 5th edition has, and continues to, sell so well. In my opinion.
What people who want the game to cater to their own desires will find, is that, one person's houserule is another person's trash, and you can't expect everyone to enjoy what you enjoy. So the default should be what's least offensive and most logical to the most amount of people. It seems a core rule just forced people to use a house rule, in order to make D&D seem more like a John Wu movie. And I'm perfectly fine with that. Play that way, you're not playing wrong, so long as you acknowledge that you are in fact not playing by the rules and allowing it via a house rule.
And yes, Wizards does get to define what the rules are, and you don't. Maybe John Wu is more popular than John Wayne these days, but I definitely see a magic crossbow in people's future that loads itself or spawns bolts already loaded.
If they don't think that reloading two weapons at the same time without a free hand doesn't make sense (as anyone with any ounce of common sense should), and they change the rules to enforce that, all it means for your game is that to John-Wu ify your D&D game you need to use a house rule to either make a fully automatic crossbow or make it so that every PC has some kind of incredible dexterity to do things that stretch the limits of acceptability.
I for one am glad this type of gameplay that ignores common sense is further relegated to house rule territory, and out of the default. Because it means my own bias for verisimilitude is being taken seriously, and they earned my investment in their product, and will likely continue to. In this case, if they have to choose between your game style and mine, as the default for D&D, I'm glad they picked mine. I'd prefer letting a PC seek out some tinker gnomes to make this kind of weapon for them, than have it be available at every corner Ye Olde Weapon Shoppe for 5gp.
If I'd have one in my game, it would cost 500gp and be a masterwork weapon. Which could then be enchanted for another 500gp if you're willing to free the gnome's kidnapped kin.