Control of Constantinople and the Turkish Straits had been a strategic aim of Russian governments since at least the 17th century. It would allow Russia access to the Mediterranean, for both military and economic purposes. As to why Greek Armies couldn't be used, Greece was neutral and remained so, albeit in somewhat of a state of civil war from 1915-16 onwards, until 1917. Regarding the ANZACs, they were far outnumbered in the Gallipoli Campaign by British and French & French Colonial troops, and Indian troops made up a sizeable contingent.