Polynesians had agriculture, but they also had limited natural resources on account of, well, living on islands, and limited arable land. They developed extensive trade networks to overcome these resource limitations[0], but their migrations tended to occur when overpopulation led to warfare.
On the agriculture - fun fact, the staple crop of the Polynesians who settled New Zealand was kumara - a sweet potato. Sweet potatoes being native to South America.
[0]https://www.popularmechanics.com/technology/a21796/ancient-p...
It's likely was that people clustered in dense settlements around natural assets like good hunting and fishing areas, or sheltered areas. Control of those would have almost certainly generated competition and conflict.
Our romanticization of the idea of living in very low density situations is a modern thing facilitated by industrial technology, just like camping became a socially acceptable pastime once people didn't have to do it to survive.
> Did people just overhunt and overfish so they had to move on before agriculture took hold?
Perhaps. The Polynesians of Rapa Nui seem to have done themselves in that way. But more likely they were forced into migration by their own relatives when they started running out of room.
I’m sure some were for the sake of exploration (maybe wanderlust). But in the vast Pacific if you wanted tropical abundance you had the Indonesian archipelago. Why bother to search for low density land like Micronesia, etc?
Did people just overhunt and overfish so they had to move on before agriculture took hold?