You're just wrong about pre-1962 there being more than one champion.

Before that, there were two recognized championship bodies. The National Boxing Association and the State of New York. Here's the key thing. 99% of the time they agreed and the other 1% of the time the two champions were matched up as quickly as possible so there wasn't any disagreement.

Even after 1962, the WBC and WBA didn't disagree very often through about the early 1980's. And again, when they did? The two champions were matched together to solve the problem.

From the formation of the IBF things really began to fall apart and sometime in the early 1990's champions began to stay away from each other and the belts became promotional tools instead of signs of great accomplishment.