My impression is that the blackface tone stack evolved to clean up the sound by cutting the mids that dominate a guitar's output. I remember some writer talking about the mid-scooped "California curve" back in the late 60s or early 70s - I assume that this was a reference to Fullerton, or wherever Fender had their plant at the time.
At about the same time, or maybe a little earlier, Fender added a negative feedback loop - in part to increase the clean bandwidth and in part to reduce hum. This had the unfortunate side effect of creating kind of a harsh-sounding distortion when the output stage actually gets pushed into clipping. Not as bad as a solid-state amp, but not as smooth as a tweed amp, either.
It's also interesting to note that different designers moved the mid-scoop frequency: from a low of about 200Hz in some Fender amps to a high of around 800Hz in Vox amps. That's a two octave range, and can account for a major portion of the tonal differences among amp lines.
And then there's the issue of tone stack placement. Along with the blackface tone stack design came a design change that put the tone stack - which has an average loss of 10dB to 20dB, depending upon the setting - between the first and second gain stages. What does this do? It knocks down the distortion levels - another move towards a cleaner overall sound.
There were obvious exceptions, like the '55 to '60 narrow-panel Bassman which put the tone stack between the preamp and the phase inverter. This design served Jim Marshall quite well in the years ahead and resurfaced in the Zinky-designed Vibro-King circa '93.
A lot of what passes for "innovation" nowadays is simply mining the past for the ideas that have already succeeded, and finding ways to build modern amps to recapture those sounds. Even the high gain amp designers are standing on the shoulders of people like Randall Smith and Jim Marshall.