Modern shift housing is not the same as brake housing. It uses many (I don't know, a dozen?) wires wound into a very shallow coil so that the wires run more longitudinal along the housing line rather than one wire coiled mostly perpendicular. The purpose is to make it very much less compressible, a requirement for consistent index shifting.

I don't have any good pics to show at the moment, but the difference is obvious.

A side effect is that it is very much stiffer. Depending on your rear derailleur and how tight the bend has to be between the stop on the chainstay and the derailleur body, it may be too stiff to work well. For example on my Bianchi with 1st gen Cyclone GT the housing fits into a hole in a part of the derailleur that pivots with the parallelogram. This means the cable always emerges in a straight line out of the housing no matter what position the derailleur is in; it's one of the little features that makes the Cyclone so smooth. But when the chain is shifted to the small sprocket the housing has to enter the hole on an angle when viewed from above, entering from left to right. That requires the housing to bend from the housing stop inward around the DO and then swing back outward. With index derailleur housing the stiffness would literally prevent the derailleur from moving that far.

The added stiffness also tends to pull the derailleur body backwards by trying to straighten out the loop from stay to derailleur. Depending on the upper pivot arrangement that can affect how the derailleur takes up chain slack.

The thing is, with friction shifting all that incompressibility is unnecessary.