Both light and hand crossbows take less time to reload than a heavy crossbow does.
As far as the tactical advantage of a hand crossbow, you can use it with one hand without a penalty, which allows you to theoretically take advantage of it in applications that would otherwise be difficult. For instance, a light crossbow takes a -2 penalty to fire one-handed, and a heavy crossbow takes a -4 penalty.
If you were to, say, be climbing up a wall or the like, you could use the hand crossbow with just one hand and then fire it without a penalty, though you'd still need to free the other hand to reload.
Combined with sneak attacks, which are how rogues can do a lot of damage, you can actually make good use of a hand crossbow to attack from unexpected, hard to retaliate against positions.
Hand crossbows can also be hidden with Sleight of Hand, and are explicitly mentioned in the text; light crossbows are not technically light weapons (except for firing one with each hand) and so cannot be hidden in this way.
That said, there's not a whole lot of applications where hand crossbows excel, but since 3.5 isn't a game where weapon type is going to be your main source of damage by end-game, sacrificing some damage on the die is not necessarily going to be as painful as one would think, especially since hand crossbows can still carry the same enchantments and other bonuses as other crossbows. The only other sacrifice you make for a hand crossbow is range, which won't typically be an issue because you want to be in that 30 foot sneak attack distance.
I want to challenge your approach to this. As you note, the Light property is defined like this:
Light. A light weapon is small and easy to handle, making it ideal for use when fighting with two weapons.
This property isn't just there as a computer function — it's also part of the basic description. A hand crossbow is small and easy to handle. And it is, as far as crossbows go, ideal for fighting with two weapons. You may need special practice and training (as represented by the feat) to take advantage of it, but it's undeniably better than any other crossbow for that case.
Is it true that mechanically there are no current rules which make particular use of this property? Meh. Probably so. But it does not mean the property shouldn't be there, because that kind of mechanical interaction isn't the only reason weapons have descriptions.
It might have been more elegant from a "the puzzle pieces must fit together!" perspective if Crossbow Expert said "a crossbow with the light property" instead of "hand crossbow", but I don't think that really would add much of actual value.
Of course, there's always the possibility of future features which apply to "light ranged weapons" or the like.
Best Answer
No
It is not a light weapon. If it was, it would have the Light property.
The name light is a) legacy (the crossbow, light has been in D&D since at least AD&D) and b) relative to the other models of crossbow. The name does not grant weapon properties.