Churchill did not have the manpower nor equipment to really defend Greece against the combined German, Bulgarian (although despite German ‘requests’ did not participate with troops in the actual invasions) and Italian forces - but politically he was required to do something.
Greece was wavering with support for the Axis as opposed to the Allies, with intervention it sort of forced Greeces hand, as a result large numbers of Axis men and equipment (far more than the allies lost) was tied down for the duration. The Greek merchant fleet had 638 ships totalling 1.9 million GRT (most of which was cargo ships 607). It had the third largest merchant fleet in 1939. If Greece went to the Axis camp that fleet plus the Greek Navy (although the major units were quite old) could or would be available to the Axis. This was during the first U Boat ‘Happy Time’ as well so an important consideration for Churchill with the loss of so many British merchant ships.
With Italy’s beligerancy Greece was not going to stay Neutral, Germany would deal with it either by forcing it to join the Axis forces in some way (much like Bulgaria) or invade anyway. The Balkans had a large Soviet/Russian sympathy (Yugolasvian republics particularly) so would need to be neutralised and that would include Greece.
There is still a debate about the reason for the delay in attacking the USSR - the reserves for Barbarossa (who were to take no part in the initial stages) outnumbered the troops sent to Greece (although they were not the best forces), the Rasputitsa lasted much longer than usual, during the first week of June the Polish and Russian river valleys were still flooded and impassable to the invading forces. So at most a week to two weeks (which is what actually happened) would have been the delay. By the time the Germans got to Moscow the forces were suffering from exhaustion and lack of man power, units being a shell of their former selves - much like the myth of Dunkirk - the Germans were stopped because they could not go further, but it is much better to blame some other force or nature rather than that the German army had fought itself to a standstill.
The intervention in Greece also continued Churchills theme (which he was desperate to prove to the US mostly), that wherever was threatened by the Axis he would resist, no matter the cost. This helped (along with payments and supplies) to keep other nations out of direct action (Spain and Turkey for instance).
With hindsight I can still say he had a hard call to make, Commonwealth and allied nations in North Africa was desperately short of equipment, supplies and the troops and equipment they did have were tired or worn out (high in moral though). Those troops and equipment sent may have been enough to push the Italians completely out of North Africa - although I doubt it before the Germans intervened, they may have been enough to resist the Axis advance though.
Chances are though the Greek merchant fleet would not have sailed to join the Allies (75% of the Greek freighters were sunk in WW2 by the Axis), or at least would not have joined in early on, during the most desperate days.
Hindsight and/or looking at a single action without looking at what Churchill could see of the bigger picture (including knowing that Germany was going to attack the Soviet Union in 1941) can lead to conclusions that may not be in tune with what was known and thought at the time. Its very difficult to look back and ignore hindsight and to limit a view to just that action.
Much like the Dardeneles in WW1, Churchill gets all the blame but his initial idea was to force the straights with an Anglo/French naval force carry troops direct to the capital - which (unknown to the Allies) almost succeded. The seaborne landings was not part of his original idea, Generals on the ground tend to get less blame for their failures to advance on day one.
Churchill with hindsight made some huge blunders, some which are considered blunders if taken in the wider context can be considered otherwise. He also did many great things and was possibly the only leader in Britain who would have kept Britain in the war against the Axis (the make peace lobby was quite strong in parliament at the time).