The stereotype is that 1950's television showed stereotypical two-parent, two-child families where nothing went wrong, and this was unhealthy for the attitudes of children growing up watching this. Leave It To Beaver and Ozzie and Harriet are cited as examples.
But more frequently, television killed off a parent somewhere and started the story later, with the bereft or even orphaned child adjusting to a new family situation. Rather creepily, Mommies got eliminated much more often than Daddies, though both parents getting the hook before the series started was also common.
Uncles taking care of nieces was big: Bachelor Father, Sky King, Family Affair. Dads left with the kids also seemed to be a big draw: My Three Sons, The Rifleman, Andy Griffith, Bonanza.
Circus Boy, My Little Margie, Danny Thomas, Gidget, Hank - there's dead parents everywhere. Or live parents nowhere might be a better way to put it. It's easy to see the sympathy draw, and perhaps the losing of a mother rates higher on the instant sympathy scale. Men taking care of kids also offered more opportunity for comedy. Still, it's weird how many moms they picked off here - maybe TV producers didn't like their wives or mothers or something. I can't think of any early single moms except for December Bride. Tough women left with the ranch out West came up though. It seems to be the reverse of the Dad-as-nurturer show - Barbara Stanwyck in The Big Valley winning against all odds.
Super-intact families were used more for comic effect in unusual situations: The Munsters, The Addams Family, The Flintstones, The Jetsons. Still are: The Simpsons, Family Guy. The Real McCoys and The Beverly Hillbillies both had multigenerational weirdness going, with missing relatives seemingly no problem. Maybe that was an Appalachian stereotype thing.