Because it made them 'different'.
They had brass backstraps - nothing else did.
Just like Johnny Yuma's short-barrelled shotgun carried in the 'custom' holster that was nothing more than the Model 1879 Carbine Scabbard, and the interchangeable barrels of 'The Restless Gun' and Yancey Derringer's inside-the-hatband single-shot Remington.
Then, there was Josh Randall's 'Mare's Laig', that Colt Buntline rig that Wyatt Earp carried that he couldn't draw from unless he kicked his leg out to the side like a Ninja and on and on - everything had a gimmick...
Every sponsor and prop guy was trying to make 'his' guy stand out, in an era that was starting to see a marketing tie-in with kids, and when one cowboy looked a lot like another - save for Roy and Hoppy - and there's just no describing their outfits.
Whenever you want to see 'real' Old West equipment in the old movies and TV shows - don't look at the heroes - look at the bit players in the background who got their outfits directly from the costume/propmaster.
They didn't waste money on the bit players, because they weren't the draw, so those guys wore an awful lot of the 'right' gear, and rode old saddles, too.
Vaya,
Scouts Out!