Is there a rational reason for the next to absence of turboprop planes
among aerobatic aircraft, or is this absence perhaps due to some sort
of stubborn romanticism?

There are actually a number of tubro powered aerobatic planes, think
for example of the PT-6 trainers.

For competition aerobatics however which includes lots of gyroscopic
forces, there are I believe concerns about the long shafts in those
engines and the huge gyroscopic forces at work. That would limit them
to sportsman stuff .. which is quite a restriction for a $1,000,000 +
airplane.

I suspect also the time required to spool up/down the power is an
issue.

Peter