Only three other persons have national holidays in the United States: George Washington, Christopher Columbus (who in my opinion, doesn’t deserve a holiday), and Jesus. King was the first private citizen to ever receive this honour.
People began calling for a day of memorial immediately after his death in 1968. However, Jesse Helms, Ronald Reagan, and John McCain all voted against the holiday, which caused it not to be passed the first time around. Ronald Reagan remained opposed to the holiday to the point where Congress had to go above his head to get it passed. McCain’s state of Arizona was widely criticized for being racially intolerant by the rest of the nation.
In fact, it was so hard to pass, it didn’t actually get finalized until 1983 (the year I was born).
Though Mississippi and Virginia still struggle with celebrating it (some choosing to honour the legacy of the Confederacy instead), even certain places outside the United States annually celebrate the day, including Toronto and Hiroshima.
The man was, for a good portion of his active life, a targeted enemy of the Federal Bureau of Investigation. Now, being a federal holiday, his legacy effectively shuts down all government buildings and banks for an entire day.
Your arguments for not being able to make a difference in the world carry no weight.