He may not have had much to do about the outcome or even the landing spot (which is what made Gallipoli doomed from the start IMO), but the the plan to land troops in Anatolia was simply a stupid plan considering that the British already had three assault points against the Ottoman Empire: The Sinai and Egypt, Kuwait, and Persia. They also could have have used Greece when they entered the war if they wanted to strike at the "soft underbelly," which I would argue would be Austria-Hungary more than the Ottoman Empire, considering Austria's failures in Serbia and against Russia and the early Ottoman success in Baghdad.
There is some truth to this but it is a long story. The war cabinet was very divided on it but there was political pressure for it as well. When Churchill conceived of a purely naval operation despite the growing hazards offered by submarines and mines it was a dangerous gamble. The Royal Navy tried this in the Napoleonic Wars and met with a similar result, but people don't realize how close this was. There were so many delays and compromises that a chance to seize the Dardanelles was missed. Even so, they actually cleared the last line of mines, silenced most of the guns, and the rest were running short of ammunition. Chance strikes with uncleared mines led to a premature withdrawal by overcautious operational commanders, and the Turks were able to rearm and lay more mine barrages. It seems far-fetched but the investment in maintaining these older capital ships, even taking some losses, may have paid off if they were able to blockade both straits, and threaten Istanbul. How would their troops on the European side get their supplies ? The Turkish Empire may very well have collapsed, at least on this sector. The firepower of this battle fleet is not something to underestimate before the era of high speed aircraft. "The reasons for the decision to turn back are unclear— if the British had pushed forward with the naval attack, as Churchill demanded, then Gallipoli might not have been a defeat. On the other hand, it is possible that they would simply have trapped themselves in the Sea of Marmara"
It is easy to see why a combined operation was the next logical step, but I can't remember all the details around those decisions. However, by this time the campaign was in Kitchener's hands, and the landings as you pointed out did not go well. Churchill had to go along with the prosecution of it as best he could, as long as it still offered a reasonable chance of salvaging the operation, though he began expressing some serious reservations to people.
He had been overzealous in promoting this before, now it was hard to back out. The futility of this campaign became apparent after a number of operational blunders, much like the western front at the time, but this was on a narrow isthmus far from home. (Gallipoli is a European isthmus by the way, not Anatolian.) The evacuation was the brightest day in the entire campaign, but many involved took a long fall over this one, even Kitchener. And Churchill, to some extent, was left holding the bag. Unfortunately his falling out with 'Jackie' Fisher at the height of this stress did much to damage his credibility further. Churchill didn't avoid responsibility for it, and the fact that he persevered and rose again in public life, despite other times of disenfranchisement gives him some dedication and durability we must respect.
You may be right that moving north from Greece into the Balkans made more sense, and that's where these guys went next, to rot in the 'Bird Cage' of Salonika with the reconstituted remnants of the Serbian army. As far as the other pressure points on Ottoman Turkey at the time, while this debacle was going on, the British were stymied, surrounded, and surrendered at Kut al Imara in Mesopotamia, a clear defeat, so this failed to even draw enough pressure off other fronts.
"Some people, such as Winston Churchill, have also argued that the landings may have helped accelerate the genocide of the Armenian population in the Ottoman Empire during 1915" In short, Gallipoli stands as an unfortunate stain on the record of a gifted military man, but in no way does it overshadow everything he did, or his basic integrity.
EDIT: as a final note, we should give credit to the Turkish army for an uncommonly spirited defense, the dedication of Mustafa Kemal, and the skill of Otto Liman von Sanders.