This only worked because the frame was modular to begin with, a rarity, so they could replace only the damaged part. IOW the car was built to be repairable. This increased its final cost, but means that it's still on the road today, rather than in a scrapyard.
This is a pretty safe general rule, but it is not absolute. I had a brand new truck < 6 months old where I was hit from behind in stop-n-go traffic. The insurance company did not want to total it because the repair could be made for less than the value of the total. I asked how a frame could be repaired, and they just said it can be done. My counter was that the vehicle would now show frame repair and would have no value for trade-in nor would someone other than less than reputable dealers offer a car with repaired frame damage.
So, depending on the insurance company (Progressive was pushing for the repair. I hate Flo), some will argue against frame damage being an automatic total.
How did you manage to do that? Was that in USA? I presume damage was on record with CarFax, etc. Did you tell new owner what happened to the car?
Finally - if you were able to show the car does not track correctly, wouldn't that be enough to re-open the claim and go back to your insurance company to properly fix it (most likely replace it at this point?)
You can find things on salvage titles that are literally two or three cars welded together.
The only thing that keeps me from doing that is not know what to do with that car when I do finally want to get a better car. It will have no value as a trade in, and I wouldn't want to have 2 insurance payments. Are they even worth anything as a donation?
But to answer the question, yes, even a dead vehicle will have some residual donation value (or you can sell it to a junkyard for $200-500 scrap value).
All that to say, they can sometimes straighten a body on frame vehicle. Whether this is a good idea or not obviously depends on the severity of the damage. If a frame rail is bent into a banana shape, probably not. If there's been some light shearing or twisting movement of one rail to the other, they can probably do it safely within limits. Remaining imperfections get taken up in the suspension (it's adjustable). If you wonder how they put race cars back on the track so fast, it's because they'll tolerate a lot of frame geometry out of spec if they can make it up in the suspension without otherwise compromising safety and handling.
All that said, all of your points about the reduced value of the truck are certainly true.