Problems in the execution
Simply stated, the legacy weapons are no better than non-legacy weapons, but y ou take massive penalties in order to use them. This is just poor design of the particular weapons, however; not necessarily a problem with the system.
Problems in the system
So what happens if we imagine a Weapons of Legacy where the legacy weapons are actually good?
Since the penalties to use them are massive, the weapons must be really good. Like, massively good. Plus, since you keep the penalties even if you lose the weapon, the weapon has to be even better to cover for the risk of losing the weapon, and keeping the penalties. So the weapon cannot just be good enough to cover for the penalties, it has to be dramatically better than that or you wouldn’t take the risk.
Unfortunately, this puts DMs in a lose-lose situation. They are presented with the following choice:
The player never loses the weapon; hurrah, now he’s got an overpowered weapon, justified by a “risk” that never actually happens
The player does lose the weapon; hurrah, now you have a permanently-gimped character and a player who may now be struggling to actually contribute and, ya know, play.
Both answers are pretty awful for most groups. A few groups might be able to take the loss of the weapon in stride, but even then, it makes creating scenarios that reasonably include everyone (including the crippled character) much more difficult. So the DM really doesn’t want to take the weapon away, but then the weapon becomes overpowered and everyone needs to have one just to remain on the same playing field.
This is actually seen in the Item Familiar option offered in an issue of Dragon magazine; the Item Familiar is really good. Many DMs ban it because they do not want that lose-lose situation.