What really happened at Easter Island remains controversial.

At least, one would think, when the larger trees had all been used and they could no longer build canoes to connect them back to Polynesians on other islands, or to fish, they would have stopped for a breather and taken stock.
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From the Wikipedia article:

The cult of the birdman (Rapanui: tangata manu) seemed largely to blame for the island's misery of the late 18th and 19th centuries. Contradicting these "legends", however, Katherine Routhledge (who systematically collected the island's traditions in her expedition in 1919) showed that according to the natives, all these conflicts and misery are precisely dated to the period after the arrival of the Europeans. Regardless, with the island's ecosystem fading, destruction of crops quickly resulted in famine, sickness and death.

and

In his book A Short History of Progress, Ronald Wright speculates that for a generation or so,[when?] "there was enough old lumber to haul the great stones and still keep a few canoes seaworthy for deep water". When the day came that the last boat was gone, wars broke out over "ancient planks and wormeaten bits of jetsam". But this statement is flawed since the sea going craft the islanders used were not made of wood, but of bundles of freshwater reeds planted in the Rano Kao crater which, according to Wright,...

Also there has been evidence that part of the deforestation was caused by climate change.

So I agree with j.mills that there is no reason to think what really happened is all wrapped up.