Output coupling capacitors in dual-supply op amp circuits
The capacitor would have to be terminated with a resistor to ground.
  To avoid loading the output, it would have to be a high value resistor
  and this would introduce additional noise at the output.


Not really, a 1 Mohm resistor might introduce 18 uV across the full audio bandwidth (see this calculator) at ambient temperatures of 20 degC but this would be into an open circuit. That 1 Mohm resistor would not "see" an open circuit - the input impedance of the following stage might be 10 kohm so that turns 18 uV into 1.8 uV but, even then the driving amplifier at frequencies in the audio band would have a substantially lower impedance of a few ohms.

A 10 uF series output cap and 10 kohm shunt produce a low frequency 3 dB point of 1.6 Hz so there isn't even a problem about choosing an electrolytic because a neat little SMD cap will do the job.

So ,if the input impedance of the unknown next stage were 1 kohm, the low frequency cut-off would rise to 16 Hz - is this really an issue?

So how big could the offset be for a unity gain op-amp - maybe 5 mV - if this were put across a 10 ohm resistor there would be a current flow of 0.5 mA and would not really trouble nearly all op-amps capable of working to 20 kHz.


  Is there anything I'm missing here?


Putting things into perspective? Considering reality? Provoking me to answer your question (by raising it LOL)?