Tim, it could be an Ahmedoodle bird - the bird without legs that had trouble landing. He could soar like an eagle but couldn’t run with the turkeys and every time he landed, he said, “Ah me doodle.”
I’m not sure the average shop could cut a perfect section in a triangular form over the length of its profile. Its doable with CNC, but that no guarantee. Whereas, the old round section takes a lot to stuff up. A common problem with fluted barrels was the uneven flute, some cut deeper than others, as a former Australian Team to South Africa found with a few barrels, (obviously poor QA and pre- testing). Probably more due to barrel curvature, than centre to centre line up on the jig. Also, would the triangular profile suffer more from minor bore wander, as round barrels which are turned between centres still have a fair bit of meat for a decent wall thickness to mitigate against this problem if it does occur? The triangular profile has both thin and thick walls.
The other thing I would be curious about would be the vibration pattern and the relative stiffness. It could be the super centre was in the shape of a triangle to match dispersion patterns.

Just joking. It may have some merit in the sunshine if mirage heat from the barrel was dissipated away from the barrel centreline to enable a clearer view of the target. Would it perform better with a flat section indexed on top or bottom? How would the barrel respond to wind buffet with its flat sections? How would it perform in a compensation tune? I suspect not well. Its from 700 to 1000 yards which could benefit from more research. There would be added difficulties in changing the taper and keeping it uniform and as such a straight taper would be better. David.