You can certainly dual wield crossbows with the Crossbow Expert feat. As long as the crossbow is loaded you can fire as a bonus action. If you have both crossbows already loaded you can fire one with each hand. Knock yourself out. You can't reload without a free hand (usually) to draw the ammunition but you can, in fact, dual wield loaded crossbows with the Crossbow Expert feat.
Come to think of it, you can even dual wield without the feat, too. You can't fire both crossbows in the same turn, but you can do it.
I guess it never occurred to me (or to Crawford, apparently) that people would think you somehow didn't need some way to draw ammunition.