Lori Erica Ruff is an exception - left due to stress (her parent's divorcing - certainly Maura was under a lot of stress as well.) But she got her new identity pre-9/11 when this was very easy (find a kid who died very young, order a birth certificate, claim to be them and ask for a SS #.) Frankly we don't know how many people did this - if they didn't find the lockbox after Ruff committed suicide, how far would the family have looked at her past?
But I don't think Maura would have been able to do the birth certificate thing in 2004, it had already been closed up and everyone was a lot more careful about false identities. You can't live a comfortable but sheltered life anymore like Ruff or Chandler, 14 years is a long time to live off the grid.