Why is downloading a native app easier for Average Joe than clicking a link to a web app that's served with appropriate Cache-Control headers and uses localStorage?

Cache-Control gets ignored when browser tabs are "paged out", especially on mobile. It's egregious on Mobile Safari, where effectively only two or three pages are "live" and the remainder have to be re-grabbed. No connection? No re-grab. The version fetched might be any version from any point in history, including your "does this work?" flight that you pushed (because of course you pushed one). There's also very little mechanism to tell ahead-of-time whether a network request will work - you'll have to essentially pre-flight all server communication, which is doable, but not easily accessible the way that a "save locally, upload in background once internet" would work as a native app.

As an alternative to having them download a separate app, have them download a browser that supports the stale-if-error Cache-Control directive. It's fair to ask people doing serious work not to use Mobile Safari.

It's also fair to ask them to keep checking the native or web app to make sure the data was sent, so one doesn't have to rely on web workers staying alive in the background. Just save to localStorage, catch network errors and keep retrying.

How haven’t PWA disappoint you

But these are precinct officials, who took the time to become volunteers in this. They should be able to spend 1/100 of the effort that would take them to file taxes and preload a webapp.

From my experience with volunteers in different non-tech areas I have doubts.

If they can't open a web page they also are incapable of doing the math required on the sheet before sending the results.