Your coin has a lot of remaining detail and luster, but it is still only an AU Jefferson Nickel. And although there is excellent step detail, Jefferson Nickels need to be mint state to qualify for the full step designation. I think your actual confusion is your definition of near perfect. The coin shown below is near perfect. You can compare & contrast it to yours to see the difference in quality.
I’ve never seen an impaired proof with that many marks and the steps should be even bolder on a proof. Early 60’s Nickels are rare in full steps but the 62-P is one of the easier to locate with good step detail.
The rims just looked a bit square to me. The step detail was good, (which always makes me think proof), and the marks came post-Mint. That said, I didn’t think 62s had good step detail, so, I learned something by asking.