John Wayne wore a belt because he hated how high-waisted trousers looked on him.
I believe you can reference that in the Harry Carey Jr., book - 'Company of Heroes'.
Don't use the 'John Ford Reference Library' when researching the 'real' Old West.
It only applies to Hollywood's version.
Trouser of the time frame were beltless - insofar as loops were concerned.
There was an adjusting belt at the very back - and no more.
Suspenders were in common use - but those who didn't like them - for whatever reason - would simply tighten that little belt in back and let it do its work.
The easiest way to produce an 'authentic' pair of trousers for C&WAS is to buy a new pair of Levi 501's - remove the belt loops and the left rear pocket -clean off the loose threads - install suspender buttons - wash and wear.
Without a crease.
Good luck.
Scouts Out!