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The article Following the airport paper trail: Where do Department of Agriculture declaration forms go? gives the following explanation for the process:
By law, the forms must be handed over before any passengers or bags exit. The envelope goes from gate agent to ramp agent, through the baggage maze to an Ag Department employee. That worker walks it through baggage claim, to another AG inspector to be checked by hand. That's the first step of their journey. Every single envelope from every flight picked up ends up at Fort Street Mall at SMS research. Every AG form is scanned and stored electronically forever.
Unfortunately the article didn't go into more detail on what exactly said AG inspector is looking for - i.e. lets say someone declares they're bringing 20 kilos of bananas in their luggage, what would they do with this information given that you can just pick up your bags and walk out of the airport without everyone being forced to stop at the customs desk? CBP solves this by having an agent inspect the form for every single person coming through the international border but no such system exists in Hawaii.
So in practice... the form is used in three ways:
The text reminds you to stop by the quarantine inspector on your way out to show what you have in your luggage:
Please submit all of the above-marked items in your possession and/or baggage for inspection to a Hawaiβi Plant Quarantine Inspector in the baggage claims area.
Whether or not you fill out the form is sort of immaterial at that point - the inspector will take a look at what you're declaring and let you know if you can keep it or not.
To make prosecutions easier to handle. If they catch you during a random inspection in arrivals and figure out you've lied on the form, the prosecutor now has two things to try and convict you with.
To collect data about visitors. The reverse page of the agricultural form contains a detailed survey on what your plans are in Hawaii. And even if you don't fill that out (as its optional), they'll still get useful information from knowing where you live, where you're staying in Hawaii and how many people are traveling with you, as that data is on the mandatory first page. This does have some privacy issues as the forms are processed by a third-party company and are permanently kept on record.
Interestingly as you leave Hawaii, your luggage is always scanned prior to checking it in to look for agricultural items but this doesn't apply on the way out. Hawaii has been complaining about this since at least 1992 with little success.