Maybe he is doing it so that can inherit the Crown Prince title after his father passes. That I don't understand, if they want to keep their royal titles, well, ok, 0but the Crown prince title is usually reserved for the next in line to the throne. Since there is no throne and no Crown they should dispense with it, imo.
I think the 'Crown Prince' title will go when Pavlos does because - as you rightly note - there is no throne or crown to inherit. Constantine-Alexios will be a 'Prince of Greece and Denmark' and the acting head of the family once his father dies.