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There's a few reasons for it to exist. One is to limit voltage differential between primary and secondary of the power transformer and prevent it from shorting, another is to RF ground the receiver...The neutral of the most outlets is tied to ground at the breaker panel and you can use either as a ground. If the cord is unpolarized and connected backwards there's still some ground reference for RF reception but there's an extra 10-1000 ohms across the radios transformer and utility transformer windings to ground.
That resistor isn't exactly essential but it's good to have present.
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