All of these are excellent reasons. I think the trouble most people have with this is that they think you average in just because it went against you, like someone shorting Tesla, and we clearly know how that turned out.Context is more important than precise entry. And probability works in ones favor very often when averaging down (depending on the context) and by averaging down you can avoid missing a trade trying to get a precise entry. Plus if you at least get a position on and it quickly moves in your favor you at least have a position on when if you wait for a precise entry (which really doesn't exist) you may miss the trade entirely. Finally, averaging down if done right, can increase ones's win rate dramatically which at bare min is a psychological boost and often leads to big profits.
I don't have the math or rules worked out nearly as well as you do, but I see over and over when I analyze my trades how many would benefit from a scale-in vs. a stop-out. Yes, some would have turned into a disaster. So lets say instead of an NQ trade costing me 10 points, it ends up being a 50 point loser once the scale in is factored in. But there are so many trades that were 10 point losers, which would have been 10 or 20 point winners with the scale-in, and so especially because a major support or resistance level wasn't breached. Those will more than compensate for the big loser.
I think the problem is that for some traders, it won't be a big loser, which is still manageable, but rather a gigantic loser that comes about from a margin call or hoping and praying. So the issues isn't that of scaling into a loser, but having no rules for how to exit when it isn't working.