With a "pinned" mortise and tenon joint, it's not going to be the pin, round or square, that fails - it's the wood between it and the end of the tenon that will fail if the joint is subjected to enough Pull The Tenon Out Of The Mortise force.
With modern glues, there have been plenty of tests that show that, with a properly fit mortise and tenon joint, it's the wood fibers on one or both sides of the glued surface that fails, the glued interface is stronger than the adjacent wood fiber connections.
Now about the pin - square peds, oriented so a face on the peg is square to the grain direction, it will distribute Pull Apart forces over more surface area of end grain - than would a round peg - which concentrates forces to a single point.
But backing up, who here is building furniture to hold up to normal day to day forces - for a hundred or more years? And if that is the case, do you think the piece will be valued highly enough to be cared for - for 5 generations? People move two or three or more times in their lifetime. And over five generations there's bound to be changes in the temperature and humidity the piece will live in over the 100 years. And over that 100 years, tastes will change and unless the piece is a Maloof or a Krenov and has not just senitmental value - it's going to leave the family at some point - and become just another piece.
I'm for making things I can use and looks good to my eye. After me - I won't be around to have to fix it if something loosens up.