On the other hand the very geometry and small size leads to compromises, and things like connecting resistors etc. must, in reality, be semiconductors -- not metal film, carbon film, etc.
This isn't true, I use thin film smd resistors which are very easy to find and there's a much wider range of C0G/NP0 capacitors available in smd than through hole. If you look at a datasheet for an op amp the design is likely to be an entirely straight forward transistor based amplifier in a small package.
Small packages have significant advantages in audio applications, the feedback loop from the output to the inverting input of an op amp can be reduced to a few millimetres which results in improved accuracy. Also IC's are very accurate in their own right as components such as resistors can be laser trimmed and very precisely matched. The drawbacks really come down to heat dissipation and the voltage handling capability. Small packages have a small surface area which requires effective heat sinking... which if designed properly will work fine. The other drawback for the designer is that the maximum rail voltage is likely to be dictated by the IC, so if you want +-60V rails you have to go for discrete.
There are many ways of optimising the performance of ICs, at the moment my favourite is to use a power amp IC in the feedback path of a precision audio op amp.