Narsil is just reforged - its not fundementally changed.It's been a LONG time since I read the Drizzt books, but I seem to recall that he upgraded his gear regularly enough. Aragorn had level-appropriate weapons (though to be fair, he was probably only level 6). Luke had the equivalent of a +1 Adamantine Bastard Sword that deflected blaster fire, and in the film Conan The Barbarian, Conan uses a magical sword that he found in a ruin throughout the majority of the film. These guys really weren't any slouches in the equipment department.
And interestingly enough, the "ancestral swords" that belong to Aragorn, Conan, and Luke all end up being destroyed, lost, or used to make new swords. At least amongst these characters, the common trope seems to be that these heroes are forced to forsake their father's weapons and must either find or create their own sword in order to make their way in the world. Aragon's busted sword is used to create an entirely new weapon, Conan actually sunders his father's sword in combat with Rexor towards the end of the film, and both of Anakin Skywalker's lightsabers end up falling into chasms, never to be seen again.
Conan - what of the books? Howard is canon, anything else is "Not...really."
More to the point, none of them are overly dependent -on- their equipment, which was the point I intended to make - yes, they do have pretty nice stuff, but its not necessary just to keep up with opponents of their level.
Assuming for the sake of arguement that it isn't a matter of imbalance amongst the PCs - why the hell not?The problem is that if they start off with the weapon at the beginning of the campaign, it's going to need to be much, much weaker then a weapon that would be used at the highest levels of play. If the character finds his father's weapon later on in the campaign and is all magicked up, it can still be fairly competitive. But most GMs are not going to let a 1st level character start the game with a +2 Defending Bastard Sword. They may, however, be inclined to let the character magically upgrade a Masterwork Bastard Sword over the course of the campaign in some fashion.
No, really. High level items requiring being high level doesn't make sense at all here.
As for Drizzt: As I recall, he recieved a scimitar from Mooshie at some point before settling on Twinkle and Icingdeath (his originals having broken).
Not that this matters, I'm just observing while we're talking about the equipment he has.