Yes. But exchanges and businesses could still wait until there's 1040, 2080 or 10400 before they take your fresh coins if they don't want the risk of transaction reversal.

We could make the standard wallet freeze coins for that much longer, so they can't be put in outgoing transactions. If someone receives "fresh" coins, they know the other person is going all the way to use a hacked wallet which immediately flags it as fishy.