The Blessed Virgin Mary was conceived without sin because of the dignity of the holy Child she was chosen to bear. As you rightly point out, Jesus Christ did not need a sinless mother in order to be born sinless Himself; Jesus could have been born sinless even if his mother had been an unrepentant lying, blaspheming, murdering, thieving adulteress. Mary’s sinless conception was not necessary but fitting, as it was fitting that the stone tablets inscribed with God’s words, the Ten Commandments, be carried in a new wooden container covered inside and out with precious gold even though an old container previously used to haul muck from stalls could have been used to carry them.
An understanding of how the Virgin Mary’s sinlessness fits into God’s plan of salvation also makes a lot of sense if you understand, as early Christians did, that Mary’s obedience countered Eve’s disobedience. Just as St Paul compares the sinless Jesus Christ to Adam in Romans 5 and 1 Corinthians 15, very early Christians, such as St Justin Martyr (Dialogue with Trypho, Chapter 100), writing about 155, and St Irenaeus, (Against Heresies, Book 3, Chapter 22; Book 5, Chapter 19), writing about 189, compared the Virgin Mary to Eve. In one place, Irenaeus concludes, “And thus also it was that the knot of Eve’s disobedience was loosed by the obedience of Mary,” and in another, “And thus, as the human race fell into bondage to death by means of a virgin, so is it rescued by a virgin; virginal disobedience having been balanced in the opposite scale by virginal obedience.”