This discussion looks to me to have focused on the tactical more than the strategic.
As most people on this board probably know, it is said the British seizing Agincourt and Erin for their own purposes, instead of delivering them to their original purchasers the Ottomans, cheesed off the Turks. But it was Souchon's ships reaching Constantinople, and "joining the Ottoman navy", more-or-less as replacements for the missing battleships, and then Souchon's self-initiated attacks in the Russians in the name of the Ottomans, that firmly and conclusively brought Turkey into the war on the Central Powers side.
A few years later, the Gallipoli campaign produced approximately a quarter million casualties for each side
So, if Troubridge's cruisers had engaged Goeben and Breslau, and all four armored cruisers had been destroyed with all hands lost, but they had slowed down the German ships long enough for Milne's three battlecruisers to have caught up and sank them both without them ever reaching the Dardinelles, then, in the big picture, the British nation would have been the better off.
In fact, I think that a case could have been made that if Souchon's ships had both been sunk but they had first somehow sunk the entire twenty-five ship British Mediterranean fleet - battlecruisers, armored cruisers, and all - even that might have been an overall more favorable strategic outcome for the Allies than what actually happened IRL.