There are so many "classic" cartridges to choose from, it was difficult to sort through the wishes of all the members here. Certainly the .25-35 is a great choice for a Handi, as are the .25-20 and .32-20 rounds. I imagine a case could be made for virtually any of the current pistol and revolver cartridges. I suppose that any rimmed case has its adherents.
Then there are current and former military issue rounds. I for one would much rather have a 7.62x54R Handi than a .30-06 Handi, but that is part of what makes horse races, right? A strong point in favor of those chamberings is availability, and indeed, four out of our past five G.I issues are current Handi offerings. We just need that darn .30-40 Krag to make it complete. Oh, and the .50-70 Gummint!
For the most part, I fall strongly into Larry's camp. I am not entirely certain the .25-06, .270, .280, .30-06 class should be chambered in a Handi. There are quite a few reliable posters (like Larry) who have reported stretching issues in the past. That is why I tended to choose milder cartridges for the most part.
Frankly, I would have even substituted the .250 Savage for the .257, but there was less of a call for it. And the .25-35, while one of my favorite cartridges, just didn't have the numbers of past posts like the .257 Bob to justify inclusion, although it is pure plumb perfect as a Handi chambering.
If we have to explain the "need" for a certain cartridge, or justify the ballistics, then there isn't much point in suggesting any cartridges, y'all just don't get it. I would have to say that, yeah, I could get along fine with three or four. Well, maybe five or six!

But that would make this hobby boring...to me.
There can be no pleasing everyone, and I was trying to be realistic in my choices. I honestly did look at many back postings for suggestions, but it doesn't matter in any event, you can see that the poll is slowly dying. Quite a few folks posted that they didn't see the cartridges THEY were interested in, but there is no telling if those choices would have inspired a better response either. Unless you want to make your own poll, we will never know.
Maybe if we are lucky, someone at a distributor will have watched this and run with the idea, or maybe H&R will try a limited run "classics" program. But I wouldn't hold my breath......