You see, I go just the opposite.
I don't believe there is a good "generic system" and I don't think there should be a generic system.
I prefer a system that emulates a specific (or at least a type of ) setting, rather than forcing a setting to conform to a given set of rules. This is an important concept to me.
One of the problems I find with systems like Heroes, GURPS, and the like is that they are flavourless -- in trying to do everything concievable, from Grim And Gritty to Wuxia, they became incredibly vague, thus, to my mind, do nothing particularly well.
Now D&D is not a generic system. D&D does D&D very well, but no other fantasy setting at all, to my mind -- not Arthurian literature, not Tolkein, not Conan, not Earthsea, not Game of Thrones. Instead, you are expected to shoehorn the "realities" of those settings into the odd tropes of class, alignment, level, XP, and suchlike, which tends to leave the settings looking very odd and not very much like their original vision. On the other hand, if you want to emulate Eberron or the Planes, D&D does a fantastic job.
So, yes, I'd rather that D&D be honest with itself and be D&D -- don't try to be generic, don't try to be Arthurian, Classical Mythology, or anything else. Eberron was a good example of what D&D is like -- a world that actually fits the underlying principles in the rules (a rather backwards way of creating a world to my taste, but still ultimately quite valid).