You still can freeze accounts. You merely maintain a list of "frozen" addresses, and anyone who accepts payment from them is guilty of a crime. It's actually much easier in this scenario.
Once nobody can tumble legitimately then quite literally only the criminals will tumble and there you go.
Really, you can dictate whatever you want as this central authority, but enforcing it is a whole different matter.
That could never happen in a free country.
Also there's nothing stopping someone from evaporating the coins via mining fees. So you'd have to have dictatorial control over all miners as well.