While I understand the need for creating higher-level characters to join an existing campaign, I don't like starting a new campaign with PCs above first level (but, in my opinion, a first-level fighter is still a Veteran). Part of the problem with starting PCs at higher levels is that their background typically does not include stupid rookie mistakes, and those are such a vital part of any D&D game. A good player might make up some humiliating experiences or mistakes in the background ("I chased the little thief into the ally and then I was ambushed by fifty Jermlaines who knocked me senseless and took my armor...").
A second issue is that the player has to work quite closely with the DM on the backstory. "No, you didn't encounter a rust monster previously, and you have no idea what they look like; no, you didn't kill one the Frost Duke's guards, and I can't tell you why." Related to this is the fact that, when starting a new campaign, the DM may not have enough of the world really fleshed out to give every character a detailed adventuring career as backstory, and may wish to have everything be as new for the PCs as it is for the players. Just something to be aware of.
The low-level experiences do shape the character a lot, and I do like them, so I think it's a shame when they have to be done away with... but sometimes it is necessary. Again, I do consider first-level characters to be accomplished, considered adults by the community, and finished with their apprenticeships.