Let's say that back in 1930s when they were assigning frequencies for the broadcast television channels, they allocated enough extra bandwidth for a future color (chroma) signal, apart from the existing monochrome (luma) signal.
If the bandwidth was available, would it have been possible to include separate chroma and luma components in the broadcast signal without the two interfering with each other, thereby producing a much cleaner color image while maintaining backward compatibility with the original B&W TV sets?
Isn't that essentially what happened? In the 1930s, the channels were allocated at 6 MHz spacing, but only needed about 3 MHz of bandwidth for the luma channel. There might have been some foresight involved, but the gaps between channels also allowed for cheaper, less precise tuners. Then in the 1950s they added a 1 MHz chroma signal on a 3.58 MHz upper sideband, expanding the channel bandwidth to just under 6 MHz.
6 MHz was there from the start. If it wasn't, the CBS field-sequential might have won. Both government (FCC) and industry (RCA) were pushing for a backward compatible system and there was enough bandwidth to pull it off. OP asks what would've happened had chroma been given its own separate, non-overlapping band. That was not possible while maintaining compatibility.
You could argue that if extra bandwidth were available it might be better allocated elsewhere for improved picture quality. But yes. It would've reduced lots of engineering complexity and probably would've looked very much like PALplus.
Let's say that back in 1930s when they were assigning frequencies for the broadcast television channels, they allocated enough extra bandwidth for a future color (chroma) signal, apart from the existing monochrome (luma) signal.
If the bandwidth was available, would it have been possible to include separate chroma and luma components in the broadcast signal without the two interfering with each other, thereby producing a much cleaner color image while maintaining backward compatibility with the original B&W TV sets?