Usually audio inputs use protection diodes that shunt into the power supply rails of the device they're protecting. But is this really necessary? Why are TVS diodes not used here? Yes, some are high capacitance. But they have low capacitance parts that are ~3pF or less for DSL modems and such. If a TVS diode can shunt from input pins to the chassis at the entry point of the enclosure, would that not be better?
TVS is for power section of electronics. Small signals that are forwarded to amplifiers would suffer from leakage currents. A high impedance of amplifier input has to be protected by low leakage diodes, less than pA. A JFET transistors are used as diodes, range of 100fA (femto amperes).
Linearity. Pro audio electronics designs measure distortion to about 0.001% or less at around 20V peak. Anything that might reduce the circuit linearity, and introduce a bit of distortion, is not desirable. Any kind of diode from signal path to ground might do just that, but especially that has quite special behaviour to transients like a TVS.
Consider that the input might be driven from a source impedance of about 100R, if you want to put a device across the input which changes resistance dynamically, you need to know that that resistance remains well above about 100k, under all "normal" input conditions, even as the device ages. This doesn't seem to be the type of thing that is really specified too much on a TVS datasheet, so most audio designers are going to play it safe (especially considering how picky and critical some of their less-informed customers might be).