Like Easter Island.
Had the natives used a handful of trees for ships, they could have gone to the mainlaind, harvested trees from there for the erection of those giant heads, and kept their own island (read "planet") pristine.
I wouldn't say they deserved to die. To keep in-universe, you might remember the Kelvin species having the ability to turn people into small cube-like forms. Power-free stasis! In Spocks Brain you see a weapon that can also stop mobs even not when line of sight.
This might be the key to overpopulation. Immobilize some to keep them from starving. Procreation may be limited, and the cubes thawed out as it were on an as need basis--and to reduce the size of ships for space exploration.