This kind of error is easily avoided if you know just a little something about Greek, or even how to do word studies. The first option is simply to look at other translations. They almost all say, "Greetings." This is the first indication that you have misunderstood the significance of the word "Hail."
The second is to look at all the other places the King James version uses the word "Hail." Other than references to frozen rain, most of the uses are during Jesus's trial where the language is highly sarcastic. However, in Matthew 26:49, Judas betrays Jesus by saying "Hail." In that context, Judas certainly was not calling Jesus "King."
But the easiest solution is to find the Greek behind the English and see what it means. There are multiple ways of doing that, but the easiest is using a website I made. And it's free. Go to my website, BillMounce.com, and choose the option "Greek-English Interlinear Bible" in the main menu. You can also go directly to bible.xojocloud.net. This is the screenshot shown above.
You will see that the Greek word translated "Greetings" is χαῖρε." If you click on the word, the Concordance button appears below with a fuller definition.
If you click the Concordance button, you will see all the places the Greek form appears.
χαῖρε is simply the common way of saying "Hello" to one person. If you were saying hello to more than one person, it would be χαίρετε. If it were a formal situation, you would say χαῖρειν (Acts 15:20); 23:26; Rom 12:15; James 1:1). You can hear me pronounce the words on YouTube.
So be careful at drawing conclusions based on one translation. Mary truly was "highly favored," and it was true that "the Lord is with" her. But she was certainly no famous or powerful personage.
P.S. If you want to do more work on word studies, check out Chapter 10 in my third edition of Greek for the Rest of Us.