There is a fierce debate on the history of Rapa Nui - whether the population was stable until European contact or if there was a large boom and bust. The evidence for the boom-bust has always seemed pretty strong to me. There are the classic arguments of the obvious deforestation, collapse of biodiversity, erosion, islanders moving into caves, etc. But there is one aspect that is, I think, underestimated: heat.
It is a small, isolated island with cooler weather than most other Polynesian islands. The heat really does make a difference, it gives you substantially higher energy requirements; most of the year mean daily temps are 60s F versus 80s on many other Polynesian islands, and the winds are strong. You will need both more calories and more heating (trees.) Then, consider that the period of collapse would line up with the Little Ice Age, which we already suspect to have caused severe drought on the island. [0] Cut down a relatively small number of trees to burn and now your crops and homes will be sprayed with salty, cold sea spray, so you move inland, and to move inland you have to cut down more trees!
There are, of course, other causes of the deforestation, but there is strong evidence [1] suggesting that the people killed the trees, not the rats. Why would you cut down trees? 1) you need more agricultural land, 2) building, 3) heat. Spend all day on a small island with strong salty sea winds on a cool day and you too would enjoy a nice big fire to warm up...
[0] https://eartharxiv.org/repository/view/6509/
[1] https://www.sciencedirect.com/science/article/abs/pii/S03054...