It's because of John Anderson's role in "The Hunter" that we can at least splain away why so many cowboys passed through North Fork all looking the same.
Cass Callicott was a legendary mountain man who unfortunately played a major role in the slaughter of the buffalo. In his final days, the old hunter became obsessed with proving he was better than Lucas McCain with a rifle - driven to the point where he was willing to kill Lucas in order to maintain his vision of supremacy.
(It was 'The Rifleman' version of "The Most Deadliest Game".)
Save for Cass Callicott, most of the other characters played by John Anderson on 'The Rifleman' were roughly the same age. Cass was far older; I'd say by about a generation, which should make this splainin "relatively" simple:
Cass Callicott was the biological father of most of those other characters played by John Anderson.
Callicott had no fixed address. He wandered the West, from California back to St. Louis. And he probably left bastard children in his wake wherever he went.
Lucas described Cass Callicott to his son Mark as having lived like a savage, to the point where he had actually become a savage. (And I'm not using that word in its "noble savage" connotation.) So I'm afraid that most of these "liaisons" were not consensual; instead, the children of these unions were the result of rape. And I imagine most of these women hid their shame by passing off their bastards as the sons of their husbands - if they were fortunate enough to have been married.
But telegenetics being as strong as it is, it wouldn't be long before those bastards began looking like their true father. (As is currently the case with the love child of Ahnuld.)
For some reason, many of the sons of Cass Callicott found their way to North Fork, New Mexico, where many of them (but not all) were killed off by Lucas McCain. It's almost as if the Universe was "course-correcting" itself and using Lucas as its vessel to rid the world of these inglorious bastards. (Work that would also be carried out by Marshal Matt Dillon and the Cartwrights, among others.)
Here's a list of the Sons of Cass Callicott to be found in North Fork in the mid-1880's:
"The Retired Gun" - Owny Kincaid
"Shivaree" - Chet Packard
"The Hawk" - Eli Flack
"The Patsy" - Sully Hobbs
"Mail Order Groom" - Jess Profit
"Face of Yesterday" - Hank Clay
"The Journey Back" - Will Temple
"Incident at Line Shack Six" - John Gangling
The two characters played by John Anderson to be taken out of contention would be John Beaumont from "The Shotgun Man", and Samuel E. Gibbs, Lucas' father-in-law, who visited his late daughter's family in the episode "Old Man Running". But "Johnny Beau" could have been a first cousin to Cass Callicott; he was certainly old enough.
With Mr. Gibbs, it was a matter of a slight physical resemblance that would have passed unnoticed by Lucas when they were reunited.
These weren't the only bastard sons of Cass Callicott. More could be found over the years in Dodge City, Kansas, Silver City and Carson City of Nevada, and other points West. He might have even sired a child in rape not many years before he died, who would grow up to encounter two adventurers toodling about the American Southwest in a Stutz Bearcat (Judge O'Brien, as seen in 'Bearcats!')
And those that had children themselves would see exact copies of the Callicott chromosome collective surface down through the generations in families like the MacGyvers. One might have become an airline pilot who found himself stuck in the prehistoric past ('The Twilight Zone'). And others could be found in TV shows ranging from 'Annie McGuire' to 'Voyage To The Bottom Of The Sea'.
(Some of the characters played by John Anderson in Toobworld who should probably be taken out of contention would be Abraham Lincoln in 'Voyagers!', FDR in 'Backstairs At The White House', and Kevin Uxbridge in 'Star Trek: The Next Generation' - unless there was an original Kevin Uxbridge before the one we met.....)
So that's the simplest splainin I have for the multiple roles played by John Anderson on 'The Rifleman', which also goes a long way in splainin away his many roles down through the generations in other shows.
It gets a little stranger with the multiple roles played by Dabbs Greer and John Milford on 'The Rifleman'......