I think that the anaesthetist is just writing based on what they see, and trying to reduce the distress of their patients.
The patients (obese and otherwise) who get through labor with heat, cuddles, TENS, gas and peth are not patients who are on the radar of an anaesthetist. The patients they see are the ones who are not coping and are distressed. And their job is to minimise additional distress to the patient.

So if you were an anaesthetist who kept seeing distressed, large women who were difficult to help, you might also develop this view, based upon a very biased sample.

There's no shortage of work for anaesthetists, they don't need to create extra!

Maybe the advice that should be given to large women is "It will be harder to get an epi in if you need one, so if you aren't managing with the gas/heat/etc then let us know earlier rather than later".