Counterpoint, the primary use environment of the application will be on a smartphone. Web applications are not even second class citizens on iOS. In a situation where the user will be entering data all night, opening and closing and refreshing, variable internet connection quality and so on, all else being equal I would imagine the ideal platform would be a native application.
I lean towards agreeing with you that a simple website plus cheap laptop would the real world best case, but I can understand why you would want a native app.
You could use local storage and make an offline web app to avoid data loss.
I agree a web app isn't great for low friction data entry, but they only enter the totals for each candidate x each round, so that'd be a dozen or two dozen short numbers for the whole night per user.
The only extra thing I see is a photo upload. Which is not rocket science from a web app either. At least on iOS you can take people right to the photo gallery or the camera.
I would really like to believe this isn't a flask app I couldn't whip up in an afternoon and polish over a week in my free time... but I'm having a hard time.
In my experience it actually means less. SWE who cut their teeth at google are spoiled with amazing tooling and processes to support everything they do.
My personal experience with google engineers is 20% code and 80% complaining that our issue tracking system isn't as perfect as googles was.
I lean towards agreeing with you that a simple website plus cheap laptop would the real world best case, but I can understand why you would want a native app.