The reality is that it’s still not that much different. Take a bass amp, add a gain stage or two, and you have a (rock) guitar amp. Omit the extra gain stages and you have a jazz guitar amp. Add power and you have a louder bass amp. Etc.So a couple things I can think of: first off (and this may be obvious, forgive me, I'm all about obvious) - artists back then didn't have the choices we have now, and had to go with whatever was available, affordable, or sponsor given - so you'll see a lot of odd choices perhaps for bass. Second, it all boils down to Leo Fender. He designed the first guitar amps that everybody used, and he didn't make much that was different about his "bass" amps or "guitar" amps. And in fact if I remember correctly it was a Fender Bassman circuit that Jim Marshall famously 'copied' for his first guitar amps. Now of course people understand a lot more about amplification and how you can design an amplifier to specialize for bass or something else, and you have more choices. But in the '60s it wasn't that different.
So back then they worked with what they had. And remember, those were the days before every drum got its own mic and before stadium PA systems became a thing and before drummers hit as hard as they could….