Why does the daily 15-minute time-boxed event called specifically Scrum?

It's a formal opportunity for a team to focus on a shared goal and to inspect & adapt their progress towards it. If the Daily Scrum is the only time that happens -- or if it doesn't really happen at all -- ask why.

Why does the daily 15-minute time-boxed event called specifically Scrum (Daily Scrum)?

If I understood your question correctly, then the Daily Scrum, specifically the word Scrum derives its origin from the game of rugby. Here's the excerpt from a google search that defines what scrum is in rugby.

"A scrum (short for scrummage) is a way of restarting play in rugby, where there has been a minor infringement."

In the Scrum framework, the Daily Scrum is similar to the game of rugby, in the sense that you are convening as a team and re-starting and planning work for the next 24hrs. Here's the excerpt from the Scrum guide.

The Daily Scrum is held every day of the Sprint. At it, the Development Team plans work for the next 24 hours.

Hope this helps.

Using the correct terminology is important for transparency, because a Daily Scrum is defined well in the Scrum Guide, whereas a "Stand up" is defined in many other ways. A lot of those defined approaches are ineffective for allowing the Development Team to inspect and adapt its progress towards the Sprint Goal.

At my company, I hear it called a "Stand up" or "Daily Stand up" more often than people refer to if as the Daily Scrum.

I do personally take care to use the right terminology, and I correct people on occasion, but it is not my highest priority; because in my company's context, we have more significant challenges that I choose to invest my credibility and time in.

If I were to get into terminology, I would sooner focus on helping people understand the meanings (and differences) of Scrum, agile, empiricism, lean, kanban, and the various workflow and performance metrics we have defined.

The term Scrum comes from Rugby. So it's like players meeting to strategize and then play. And it should be for the Development Team members, and not a status meeting where everybody confesses their sins to the Scrum Master, apologizes and then later gets chastised by managers based on a progress report from a tool management software. Those are Daily Stand-ups, annoyingly referred to as DSUs.