I'd have to agree with habilis. Assuming not too much more damage is introduced, a straight frame will take compression forces much better than a bent frame, and perhaps also torsion forces.

But, I would plan on leaving something inside whether it is a piece of seatpost, or the wooden dowel.

I looked it up, thanks. https://materials.mcmaster.ca/faculty...and%20295K.pdf

This article states - as you said - that the ductility and malleability of aluminum increases with heat. Also, heat-treated aluminum, like bicycle frame material, can be expected to be more brittle than untreated material. It's also true that, because all aluminum has some degree of malleability, it can stand some bending. It just can't withstand the same amount of bending as can ferrous metals without breaking.

Several decades ago, armored BX electrical cable contained an aluminum neutral wire in addition to the two or more copper conductors. When this cable was rolled, unrolled, and re-rolled by electricians, the aluminum strand suffered no damage. The use of aluminum in these cables was discontinued for another reason: aluminum, when crushed, doesn't have a "spring-back" property. So when the wire was clamped in a connection, the connection wasn't as secure as a copper connection.

In my junk box, I found a piece of 1/4" O.D. aluminum tubing with an inside diameter of about 3/16". I flattened it in a vise and bent it sideways by hammering against the section that protruded above the vise jaws. It broke at about a 20 degree bend. Iron could have withstood much more bending, but the AL did survive the flattening and some bending.

I replaced more than 20 windows in my house and discarded the old AL-framed storm windows, which I sold for scrap. To make them more portable on the way to the scrap dealer, I bent many of them. Some pieces had severe bends but didn't break. Not a scientific experiment, but it gave me a "sense" of what AL can endure without breaking.

So what's the practical significance in the case of this damaged frame? As it is, the frame appears bent a few degrees - very slight. Besides being unsightly, the bend may compromise the usefulness of the frame. A diamond frame, viewed from the side, obviously depends on the ST for strength and rigidity. A bent tube may bend further if stressed by riding.

No one can predict the outcome of my proposed repair with 100% certainty. The decision to attempt it is up to the OP. If this were my bike, I'd try it based on my experiences with aluminum. The frame may or may not survive (I think it will), but left alone, it may not survive either.

PS: I still would NOT cold-set an aluminum frame to accommodate a wider axle because that's compromising something that's not already compromised. It also stresses weld-joints, not just the stays.

Thank you, that makes sense and is what I needed to know.
I find it hard to visualize these things and will avoid building any bridges.