Yes, they do welcome the tourists. You are correct when stating they rely on that source of income. They are, however, also very aware that such a small island has serious limitations in terms of natural resources (which are very scarce) and in aspects such as waste disposal so they are actually inclined to maintaining a steady flow of tourists rather than let it grow freely to meet demand.

Regarding flights, night flights are a bit hard to schedule because of the flow control issue. LAN's SCL-AKL flight departs around midnight SCL time, and for a good part of the flight, IPC is THE enroute ETOPS alternative for the 787, so the airspace is off-limits for SCL-IPC/IPC-SCL flights to accomodate for that. The return AKL-SCL is actually a constraint for the SCL-IPC departure time: it won't depart until LA800 is within ETOPS range of SCL

EDIT: For the sake of completeness, to this date LAN is flying the SCL-AKL-SYD route under ETOPS 240 rules