Well, since you asked, I looked it up Duke and the way it works is that MLK Day is always the THIRD Monday of every January. I don't know WHY they decided that way, but since the 20th of January can be any day of the week, it was just a wild and rare coincidence that this year, both happened on the same day, kind of like two planets in conjunction.
So I see it really as a non-factor, but if they really want to fix it, they should make it the 2nd or 4th Monday of the month or like you say, just make it the 15th, since the 15th and 20th of January NEVER occur on the same day.
But apparently this was all worked out by some federal workers years ago, so you can't expect too much. It is now what it is.