These two are knives my grandpa made. We found about fifty knives rusting and rotting in a five gallon bucket in his shop after he passed away. I salvaged these two, cleaned them up and made some simple leather sheaths. One day I'll get a new handle for the bottom one.
This was the knife my dad carried in Vietnam. It was also left in a shed for a long time and I'm in the process of cleaning it up. Next on the list is straightening the edge and fixing the loose pommel.
Maybe I'm just an old sentimentalist, but I see a big difference between restoring a a knife and "re-making" it. In my mind, a lot of old knives are antiques and reworking them would be like refinishing a 300 year old piece chair with urethane varnish.
In particular, I'm thinking of your Dad's & Grandpa's old knives needing a new handle & re-profiling. I'll grant you Grandpa's knife isn't a Scagel, so its eye appeal & monetary value will probably go up with the new handle. However, as I see it, it will no longer be the knife your Grandpa used. It will be an old knife you reworked to look new. Something will be lost. Its history will be obscured. If years of wear have turned your Dad's knife into a recurve, won't re-profiling it take something away from its Vietnam history?
If Daniel Boone had chipped his knife on the bone of the bear he killed, that chip would be a major part of the knife's history. It would be a shame to remove it or re-profile the blade. The handle on Grandpa's knife looks crudely made, but for all you might know, maybe he made it. It's certainly the handle he used and held. That alone gives it more sentimental value (and I would argue - beauty) than anything you might replace it with.
My attitude about old knives (for what little my attitude might be worth as an opinion) is that their use & abuse over the years gives them their character. Wear on a knife is like an honor scar. It shows that the knife served its intended purpose time and again. If I gave the old knives I have "cosmetic surgery", they would no longer be old knives and I would no longer wonder as I looked at them, just what they cut over all those decades and what trials and tribulations they might have seen. Their value to me personally would be diminished.
The issue of what constitutes restoration and just how far to go with it is very contentious and there are probably many differing opinions. (That is certainly the case with cars - Ask a collector and a hot-rodder what they'd do if they found a rusty old 32 ford.) I have no doubt that your opinion will differ from mine and the knives are, in the end, yours to do with as you please.
Maybe you'd feel differently than I would, but I would have a hard time showing my grandchildren their great-great-grandpa's knife and only having pictures of what it was like when he owned it.