I've read about this premise in many places (i.e., that busyness is a coping mechanism our minds use to avoid confronting painful existential issues such as our own mortality).

And what's your take on it?

On one level, I fully agree with the stated premise.

I've always hated the expression, "I didn't have time." Everyone has the same amount of time in every day. It's just a polite/BS way of saying, "I didn't choose to do it."

If we tell that lie to ourselves, we can forget that it's us making all the choices all along.

So negative!

It's kind of a choice. We have obligations, most of us anyway are not independently wealthy.

How about, "I had more urgent things to do."

Urgent is a choice. The situations we get ourselves into lead from our choices. I take it as empowering rather than negative. In other words, if I've gotten myself into a situation where I don't have time for things that are actually important to me, it's on me to adjust that to match my own values. It's not something to dismiss.