It is "well documented" in memes and sources with an axe to grind - well, mainly one well known revisionist source. Read even just the Wikipedia page and he was clearly not solely and singularly responsible. Even the parts he contributed were probably near unavoidable. Purely from memory:

+ There had been a series of natural disasters coming one after another - a major hurricane, a flood, a major crop disease that was spreading through the region.

+ The biggest single cause of famine was the Indian princes of other Indian states closing down trade to Bengal thanks to the fall of Burma. This resulted in Indian merchants profiteering and the price of rice and grain sky rocketing. Due to the vassal nature of the Raj, these were still independent choices. Could they have been persuaded or compelled to change? Merchants profiteering maybe, the Princely states probably not.

+ Burma had just fallen. Bengal had imported much of their rice from Burma. This was the second major cause. That trade was no longer there, and it was thought likely Bengal might fall. Countless troops and Burmese refugees were flooding into the region - most of whom were ill from the trek through Burmese jungle or injured. Which would have triggered a crisis without any of the rest. Control of the sea and sky in the Bay of Bengal had been lost, and it was expected that the region might fall any moment - it was the new front line. The actions of Japan against any civilians or troops in regions they captured are well known. Had Bengal fallen the famine would have been a trivial side issue as 10x or 100x more would have died, been enslaved or raped. Compare mortality and conditions in Burma and Nanjing under Japan with Bengal.

+ Mounbatten did request aid, but at that time the UK was barely receiving adequate food and war materiel to continue the war, let alone send food aid half way around the world. The cross-party war cabinet voted not to. Had they done so the losses would probably have been colossal. Could he have turned that decision? Who knows.

+ Losing Bengal, then likely India would probably have lost the war.

All of the above should be on Wikipedia. So is Gandhi's racism and ongoing feud with Ambdekhar (writer of India's constitution, leader of the Dalits, and probably the most remarkable and influential Indian ever).

Now then. The governor of Bengal certainly made some questionable decisions, one very suspect decision and the little aid that was provided was inadequate - yet they prioritised ensuring Bengal did not fall. No one makes memes of that guy or claims his role is "well documented". Just about no one at all knows who the governor even was. Under Japan it would have been a hundred times worse. There would be memes complaining of Churchill's stupidity sending aid instead of preventing the fall of Bengal that result in hundreds of millions of deaths at the hand of Japan.

There could have been far more local action from the neighbouring Indian states. Perhaps more could have been done to require those vassal states to send aid to Bengal, but I'm not sure that could have been achieved. Perhaps Australia or NZ could have done more, yet as dominions they were voting their own choices...