Who uses an e-brake in 2020 unless manual.
Anyone who parks on a hill that doesn't want the weight of the car resting on the parking prawl in the transmission or constantly pulling on the motor mounts.
Yes, the transmission is designed for it, to a point, 3000+ lbs resting on a small piece of metal in the transmission in my mind borders on abuse.
That's also why it is typically called a 'parking brake' and not an 'emergency brake' any more.
Copy straight from the manual for a 2003 Accord:
"Always use the parking brake when
you park your car. The indicator on
the instrument panel shows that the
parking brake is not fully released; it
does not indicate that the parking
brake is firmly set. Make sure the
parking brake is set firmly or your
car may roll if it is parked on an
If your car has an automatic
transmission, set the parking brake
before you put the transmission in
Park. This keeps the car from
moving and putting pressure on the
parking mechanism in the
transmission making it easier to
move the shift lever out of Park
when you want to drive away."
To the OP, if it were me, I would just replace the caliper and be done with it. I've usually had good luck with parts store rebuilds as long as I didn't buy the cheapest thing out there. 2013 is new enough that the cores in the system should still be in pretty good shape and haven't switched over to crap 'new' calipers.