The Gallipoli/Dardenelles campaign had no strategic benefits. Churchill was in charge of the Royal Navy and choose the campaign so he could "get in on the action". Young guy, big ego, needlessly sacrificed the lifes of others. He was kicked out of the war office to prevent any further damage - he was a hinderence.
That isn't really true. The Dardanelles Straits had very significant strategic value, as they determined access to the Black Sea, in order to support and supply Russia. As well, if the Dardanelles had been taken it was thought (not without good reason) that the Ottoman Empire might collapse.
What let down the British, French, African, ANZAC and other soldiers landed on and near Gallipoli was some poor planning, poor execution in the initial phases and the unexpectedly effective defence by the Turks. Quite a number of people were held to account for failure of the campaign.
Getting back to the miniseries, IIRC towards the end you see what happened later in the war, when the ANZACs were brought under Australian command at Corps level, and Monash (may he live on in our memories) developed and successfully applied combined arms assaults bringing together infantry, armour, air, and better coordinated artillery, as well as other things like better planning and comms, to contribute to turning the tide on the Western Front. The AEF turning up in the final months (and being trained by Australians before getting into it) also played a part in breaking the Central Powers.