There’s another big reason for having it in a narrow window–to avoid the I’m-sick-now-buy-insurance issue.
As for a typo denying coverage–perhaps it’s someone trying to cover up their mistake. Many years ago my wife didn’t have formal work hours at all, she only came in when there was something for her to do. (Since she had a base salary of $0 and was paid based on what she did this was reasonable.) The insurance guy was told about her but dropped the ball. After that it was excuse after excuse as to why she couldn’t be covered. It all ended when she figured out who the guy in the chain above the agent was and called them. Presto, insurance restored.