His mission was to observe the transit of Venus. The expedition was scientific in nature first and foremost.

You’re speaking of the secret instructions issued to him by the Admiralty to locate the fabled southern continent and hopefully claim it for England. Tasman by this stage had found NZ and I think Van Diemans Land. Yes he found the east coast of Australia and “claimed” it for England. It was all in vain though, the distances were way too far for anything to come of it. To Cook at the time, it was a side trip.

There were two parliamentary inquiries submitted to the British parliament in 1779 and 1785 recommending colonisation of New Holland, but even then: well after Cook’s death, such an expedition was seen as too expensive.

Then the English learned that the French were preparing to colonise and it was suddenly a British priority to get to Australia.

I don’t see how anything to do with the colonisation had anything to do with Captain Cook. You could swap Cook out for any other ship’s captain who was taking the scientists to see Venus and the rest of the expedition plays out much the same. Cook didn’t colonise Australia. He encountered the Guugu Yimithirr people in Northern Queensland and tried to treat with the peacefully - mostly succeeding. He certainly didn’t set about killing them all.

Arthur Philip should be the person people direct their ire at. But he doesn’t have a statue in Melbourne. King George III would be another candidate that made sense. Only George III also doesn’t have a statue in Melbourne.