It seems pretty hard to screw that up so badly but clearly it’s quite easy to make a complete dumpster fire from those requirements.
https://www.theverge.com/2020/2/4/21122737/iowa-democractic-...
they used the a free tier of TestFairy that limited the number of test users to 200 and on iOS used TestFlight and did not use either the app store for the final version or make an enterprise version, and possibly could not distribute the app to the approximate 1700 users. They still would have needed to get the app through the app store approval process for general release to fix the app at least on the iOS side as far as I understand it. To fix it quickly would have just required them to go back to calling in results by voice as in past years. Don't know why they did not just do that.
They did that - but apparently the phone number for calling in the results was the same as for "help my app doesn't work", so the phone line was flooded. Unfortunately I don't have the source link to hand, so feel free to treat that as hearsay.
However, CNN had a live cross to someone trying to call in their results, and after an hour on hold, when they finally got through, the other side hung up on them while they were broadcasting live on air:
https://www.washingtonpost.com/nation/2020/02/04/iowa-caucus...
"It took an hour and a half for Shawn Sebastian to get hung up on in 10 seconds. And it unfolded on national television Monday, making the moment, in the words of some, “one of the most ridiculous things I’ve seen on cable TV.”"