It is interesting that this discussion only pops up with the CP Pavlos & family, while nobody mentions a simular issue for f.e. the Bulgarians, Don Luis Alfonso de Borbon, who puts on airs about the French throne, the Italian pretenders, the many archdukes and archduchesses or even for Pavlos' younger brother and sister Philippos and Theodora.
There are people who are much more strongly criticized for their title usage in royal watching discussions than the former royal family of Greece, whose usage of Greek royal titles still enjoys the approval of most royal watchers. Female-line, adoptive, and out-of-wedlock children of German royals are roundly criticized by royal watchers for using the royal titles which are incorporated into their legal names, when they are fully entitled to them under the modern egalitarian laws of the German state. The late Prince Henrik and the Danish royal court were widely criticized for recognizing Henrik's premarital French courtesy title of Count, when his family had used the title for centuries without the French state taking issue.
So there are indeed some inconsistencies in the discussions of titles among royal watchers, but in regard to the French and Italian pretenders, their position is not quite comparable. In France, the titles of all three former royal families and of the former noble families
receive legal recognition and protection from the state. In Italy, the legal recognition of nobility titles has ceased, but the state appears to have no issue with their widespread usage in daily life. I am not knowledgeable about the situation in Bulgaria.
You are right that the Greek issue exists too for the numerous "archdukes and archduchesses". As with Greece, the Austrian state has long made clear that their former imperial family is expected to move on from their nonexistent titles. On the other hand, there seems to be very little royal watching discussion in the first place about most members of the Habsburg family, with the exception of the family of the head of the house (who at least appear to refrain from using archducal titles when they are in Austria), the family of Princess Astrid of Belgium (who nearly always use their Belgian titles), and the family of Princess Marie-Astrid of Luxembourg (and I seem to recall that family has indeed been criticized for using the revoked titles).
IMO the crown prince and his family do not owe the country a thing. Greece has kicked the family out and has behaved appalingly towards the RF for decades. Unlike in Romania or Serbia there are few informal responsibilities that come with being the heir of the Greek throne. I imagine it is a healthy thing that they do not cling on to long lost dreams and have moved on.
I do agree, however, that they don't owe anything to Greece, considering how they were booted out. At the same time though, if they no longer want to be associated with the country, they should no longer use the royal title either - at least in such a flaunting manner for personal gains outside the country (which in the end does bear some informal responsibilities - such as at least speaking the national language and living the country, if legally possible, as the King and Prince Nikolaos have decided to do).
I am not the most knowledgeable on this issue, but it is not my impression that the state or the people of Greece are clinging to their former royal family. It seems to be the family which claims that Greece owes them the title and name of the country.
They use titles because titles are part of the family.
I understand your point and that is probably the family's view of the matter. On the other hand, I suspect that Zara Phillips for example would be roundly condemned if she used Princess Zara of Great Britain and Northern Ireland, despite being an official member of a family that still reigns over the UK and living in the country. And as I mentioned above, there are Germans who receive criticism for using their legally-acknowledged titles despite living in Germany and being legitimate (according to modern equality laws) members of former ruling families.