Keep in mind that you would need to use *16* more diamonds to make that sword. Not only that, but it has *only twice* the damage and durabilty. With that many diamonds, I could just make 9 swords, and enchant them to get sharpness 5 and fire aspect, which pretty much insta-kills anything. I wouldn't even need to worry about durability if I've got that many swords.
For this to even be a worthwhile thing, the sword would need to do 9x damage, and have 9x durability. And at that point, its just overkill (Literally). So no, I don't support.
The crux of the problem with this suggestion is that if you alter the reinforced sword to the point that it would be worth the resources required to build it, then that sword would be way to OP for the game. There's just no good way to implement this and make it worthwhile and balanced at the same time as it has been proposed.