Why do (microphone) preamp designs tend to limit opamp gain to max 60 dB?
Gain/Bandwidth product, you want maybe 50KHz bandwidth at 60dB (1,000 times), so you need somewhere around 50MHz, gain/bandwidth product (And more would lower HF distortion)... Make it 80dB and now you need 500MHz GBP, which is getting difficult if you want low noise down near DC (And is getting really bad news to stabilise at low gain).

Also consider that the noise is completely dominated by the noise for the stage having the first 20 or 30dB of gain (Do the maths), there is a lot to be said for splitting things so that the first maybe 30dB of gain happens in a low noise stage designed for low Z sources and low 1/F noise, which now only needs a few MHz of GBP and will be easy to stabilise even with weird source impedance. Then do the rest in a second stage (where noise matters less and you have a known source impedance). 

The other difficult thing is that control laws that make sense become increasingly tricky if going for a one knob gain control, a classic instrumentation stage with have a gain setting resistor varying from a few ohms to maybe a few k ohms, which if you think about it is only maybe 3 orders of magnitude, very difficult to make a reverse log pot have more range then that.