I ought to keep a index of similar subject threads. Must have followed ten or more variants on this one in the past decade.
If the objective of Anzio was to draw German forces away from Cassino front, it did not achieve its objective.
Some, but not enough to allow that defense to be defeated during the winter.
Could Anzio have been cancelled shortly before it went in? as in 20 January?
Yes. It originally appeared in a staff conference at Supreme Allied Commander Med (SACMED) memo in October 1943 & shortly after a "appreciation study" was made. Literally dozens of proposals like this were made & most never made it past the initial Appreciation paper or outline plan. In this case Churchill took a fancy to it when briefed at SACMED on his way to the Terhan confrence. By mid December it was a done deal in Churchills mind & detailed planning & preparation was underway. When the plan fell to 5th Armies level Mark Clark decided it was not for him & advised it not happen. At this point either Alexander, Clarks senior, or Clark could have stood up to Churchill & refused. It would have been the end of their career but they could have stopped it.
Some useful reading on this would be either WGF Jacksons 'The Battle for Italy' or Atkinsons 'Day of Battle' The latter includes a quote from Patton who saw this plan to capture Rome when visiting Lucas in early january 1944. He pronounced it a "suicide mission" & advised Lucas to save the last bullet for himself.
When was it clear that Anzio was going to be a liability?
Depends on who is asking. Churchill never caught on, I'm not sure about Alexander. Clark thought the plan unworkable with the ampib fleet & ground forces at hand. Patton thought so too & predicted Rome could not be captured. Lucas who understood the operation would be executed with or without him took counsel of his HQ staff, who had been present at Salerno
What could Mackensen's divisions have been doing instead if there were no Anzio?
Waiting in reserve for any random emergency. Kesselring was blessed with enough men he could keep a large reserve, which was expected back at Hitlers HQ. Repeatedly the garrisons in northern Italy were tapped for emergencies.
If Brooke had been a bit more interested in Anzio, something might have come off it, but it also seems he was 'busy' with other things.
Interesting question. I have no idea what Brookes real attitude here was. If he tried to talk Churchill out of it he failed. If he tried to provided adaquate amphibious lift for a army size invasion vs a corps, he failed as well. But. I dont know if he tried either.
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The Idea of a two division landing on the south of France achieving anything except the loss of those two divisions is nonsense. The defender has an intact rail system he can reinforce far far faster than you can unload.
Sure, a two division operation in south France would have been useless. Operation Dragoon had a two division assault, but a fleet load of follow up units. It also had a big chunk of the amphib transport formerly supporting Op Overlord. Something that was not possible in January, or later in the spring. Eisenhower decided the amphib fleet would be concentrated in the UK for Op Overlord, leaving only a token force in the Mediterranean.