I looked for some previous threads on this. Our u/cnzmur (here) and u/wotan_weevil (here) have noted that archery was unknown in Maori warfare and not prominent in Polynesian warfare. The only direct answer I could find to why this was, is this by u/Zugwat, though that is a rather old and very short and simple answer. I hope someone will explain in more detail here.

I can answer with an emphasis on the Māori case as my area of interest is the British Army's colonial campaigns, but I'll happily give way to a subject specialist when they heed the call.

Your assumption is correct in that use of archery is less prominent in Polynesian cultures, but the use of bows was widespread with the prominent exception of Aotearoa/New Zealand. (Polynesia in Early Historic Times)

There are accounts of bow hunting in Tahiti, Samoa, Tonga, Niue, and other islands (Early Tahiti as the Explorers Saw It; 1767-I797, and Early Tonga as the Explorers Saw It, 1616–1810), and later use as a weapon in Tonga (courtesy of conflict with Fiji). The bows used for hunting are smaller and weaker, in contrast to the five/six-foot war bows used by the Fijians and later Tongans. (Fiji is a Melanesian rather than Polynesian culture).

"Enough has been said to show that the bow and arrow had their most important use in fowling. [...] Its use as a weapon of war was emphatically denied." (Samoan Material Culture)

The Society Islands in French Polynesia have stone archery platforms in the sacred/ceremonial compounds called marae, where bows are fired for ritual purposes and as sport by the elites. Interestingly, it was judged on distance and not accuracy. (Archery Platforms (Vahi te'a) in the Society Islands, Polynesia. A contextual interpretation)

What is generally accepted is that archery was practised by Polynesians in the expansion period around 2,000-1,000 years ago. Firstly, there is a linguistic argument as there's a shared etymology in the words for "bow/to shoot" in a number of Melanesian cultures that used bows (such as aforementioned Fiji), the word for bow in Samoa, Tongan, and Tahitian, and the Te Reo Māori for "to spring back/recoil" (like a bowstring). A well-preserved 'war bow' dating to the time of Polynesian settlement in Aotearoa/New Zealand was excavated on the North Island in the 1890s.

The question then is, why wasn't the bow more widely used for hunting/warfare, and why was it seemingly discarded outright Aotearoa/New Zealand?

There's no definite answer, but the theories are:

1. Hunting wasn't as important as husbandry. Many islands lack significant-sized native fauna (except in Aotearoa/New Zealand and lacking natural predators, the huge flightless birds called Moa were hunted to extinction within a century), and the settlers relied on introduced species like chickens and pigs.
2. The environment, often coastal and subject to strong winds, made arrows from weak hunting bows unreliable (Early Tonga as the Explorers Saw It, 1616–1810), although this doesn't account for societies in the interior.
3. Māori warfare typically consisted of short sharp sneak attacks in low light where bows would have been limited use, but – this is me wondering – is that really the cause or the effect?

Edit: Bonus picture

1788 portrait of a Tongan king with bow and quiver.