Why don't some U.S. colleges celebrate American national holidays?

The observance of holidays in the United States is a complicated issue.

Holidays declared by the federal government are generally (but not universally) observed by state governments, which oversee public universities here. Private institutions, on the other hand, have no obligation to observe those holidays, and can choose to close or remain open according to their own decisions about what best serves their students’ needs. For example, my undergraduate institution did not take any days off from the first day of classes in the fall semester, but did provide a week’s break corresponding to Thanksgiving. It’s an unusual arrangement but perfectly legal.

It should also be mentioned that while universities have core “business hours” where faculty are expected to be present, in reality, faculty largely choose their own working hours.

Academics don't normally get "days off". Holidays are just work days by another name. Note that in the US, there are almost no National Universities (the service universities like West Point being the major exception). Most universities are actually independent of any government control though almost all have some government (usually State) oversight.

Many universities also recognize a number of religious holidays and these vary depending on the location. In New York, for example, many don't hold classes on Jewish holidays. This sometimes makes it difficult to put together a schedule meeting all constraints.

So, it varies and there is not general rule. Some holidays are more likely to be taken than others, also. But still, it can vary. It can even vary at the same institution from year to year.

The key point is that Martin Luther King Day is a federal holiday, and only the federal government is bound to observe those. State governments and private corporations are free to choose their own holiday schedules.