My question is whether there is a necessary relation between the colour that a sensitising dye responds to, and the colour of the dye formed by the dye coupler in that layer?
The relationship between sensitizing dyes and colour coupling dyes in a typical film are related only so far as they work together towards color synthesis; subtractive in this case. In other words, you could have a totally color blind emulsion (i.e. no sensitizing dye) but with colour couplers that created
celadon, or any other color you wanted. They're not inextricably linked, chemistry wise, but it's a choice governed by color synthesis theory that the red record needs to become cyan, green -> magenta, blue -> yellow.
Of course in most C41 films, the colour created by the dye coupler is the inverse of the colour which that emulsion layer is sensitive to. But is this necessary, or a choice of the emulsion chemists? The reason for the question is a vague curiosity as to whether a positive transparency film could be created that is developed by a standard C41 process, by using dye couplers in each layer that create the same colour that the layer is sensitive to, rather than its inverse?
It is necessary if your goal is realistic color. That the color record is turned to its inverse is not unique to negative films; positive films work the same exact way, so does dye-transfer, color carbon, offset-lithography, etc. This is the foundation of subtractive color synthesis and there's no other way to make a color image on a paper or transparency than to use cyan, magenta and yellow. The whole negative bit confuses things, but the synthesis is occuring in exactly the same way, with RGB layers and CMY dyes.
Think of it this way, using a positive film as our example; the red-sensitive layer records all things red, the highlights, and makes shadows out of everything else, therefore it makes sense that the shadow densities have to become red's inverse,
cyan. In other words we want the shadows to subtract red from our white viewing light. The red parts will actually be
clear in the red layer and the yellow+magenta from the blue & green layers are responsible for ultimately producing red.
If the red record became red upon developing and the blue becomes blue, etc., the result would be complete black where any two colors overlap. This is because any 2 of the additive primaries (RGB) will fully absorb the light. The subtractive primaries, or secondaries (CMY) will only create black when all 3 are overlaid, and intermediate combinations produce all the colors.
The only way that "creating the same colour that a layer is sensitive to" could work is if the layers were separated afterwards and projected on a screen with 3 different lights. This is additive synthesis. But since they are overlapping and we're shining 1 light thru them, we have to utilize the secondaries.
Hope this makes sense; let me know if something isn't clear.