Yes, it is obvious the meddling into politics was the determining factor in the deposition of the monarchy in Greece. However, Frederika seemed to be inconspicuous relating to her relationship with Greek politics. I've read that she openly campaigned against certain politicians in Greece that did not suit the royal will, i.e., right wing. King Constantine, whether he was influenced by his mother or not, was responsible himself for guiding Greece to military dictatorship or, at least, enabled the junta to take control by none other than meddling in politics.
Moreover, one prominent Greek politician, former PM?, surmised that if King Paul had lived another 10 years, therefore, Greece would be a monarchy today.
After WWI, the Greek monarchs were a cascading disaster. They conducted themselves as if it were the job of the British and the US to prop them up and more or less do their bidding. They were determined to play a key role in Greek politics, and proved to be meddlesome, tactless and inept. (The 2009 work "Greece and the English: British diplomacy and the Kings of Greece" is particularly revealing as to Frederika's disastrous role, which spanned two decades.)
Though every fallen monarchy had its die-hard supporters, after Constantine departed, Greece quickly moved on. So did the British and American governments in their dealings with Greece.
One can't say that the Greek royal family was lacking in drama and political intrigue to say the least. However, many have accused Frederika for giving her son bad advice which said advice was partially to blame that subsequently ended the monarchy in Greece.
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