We need to remember that Greece had tried to remain neutral until they were attacked by Italy in October 1940. Once they were attacked, the Greek army was hard-pressed to defend the country. Greece lacked an organic arms industry and they relied on receiving captured Italian weapons from the British. British success in North Africa against the Italians helped to sustain the Greek defense.
The Italians had given the Greek government an ultimatum, but did not even wait for a reply and attacked from Albania into Greece. The Greek army was not a pushover, because if they had been, even the Italians could have succeeded. They fought a war through the winter, where the Greeks eventually made inroads into Albania. The Greeks ignored any threat of attack through Bulgaria by Germany.
After the British came in to support Greece by taking the islands of Crete and Lemnos, the Germans determined to end the campaign in Greece, so that they did not have a distraction in the Balkans while they were preparing to attack Russia. That alone doomed any British attempt to aid the Greeks by sending troops. They British and Commonwealth forces that were available were a fraction of what Germany was able to commit to the campaign. General Blamey and his prime minister were correct that sending troops to Greece would fail and would jeopardize the defence of North Africa. The British ignored sane advice and bulldozed their way into the disastrous Greek Campaign.