It is probably fairly irrelevent to the custodial parents whether this is so or not because unless they do something seriously wrong their position seems fairly invulnerable.
I have argued this debate a number of times on parents forums in the UK only to be told by a majority of them that they don't want legal rights for parents because that conflicts with the paramount principle of "child's best interests" (it was probably mainly custodial parent who were also mothers saying this I think).
So there it is for you, I completely agree with your assessment - I'm still learning myself of course, but only seem to be finding more evidence of how little I counted as a father, whether I was any good or not.
Graham