Maybe because calling something Independence Day that doesn't actually occur on a date independence was won seems weird? And Declaration of Independence Day is too long? Also, American culture has since the Civil War in general moved TJ out of the spotlight in favor of more "neutral" military victors like Washington and Lincoln. This is due to a host of cultural factors that don't evenly fall on to one side of the culture wars, because most things are more complicated than that.

(but if you're asking me, which admittedly you aren't, the main benefit to the Powers That Be is the very liberal idea of rewriting history to pin the evils of slavery on one founder - a sort of historical queen's sacrifice, if you will. Keeping Washington and Lincoln as pure as possible is very important, because they are both first presidents in a way, and both won that status through military victory. Keeping civilians associating the military with neutrality and the practice of voting is necessary to creating a world where liberals are easily bullied into accepting, and then actively supporting the management of, the invasion of Iraq - liberals who then howl doomsday because they are truly convinced that Trump will involve us in unnecessary war)