... it would be broadly comparable with the situation in which a DVM gave a non-zero voltage reading when there was no pd between its probes - which is certainly not something I've ever seen happen.
But how do you know you've never had a situation where you've had a non-zero voltage under reported ?
On the contrary, I know that I have had (faulty or cra**y!) meters which (by comparison with others)
have under-reported non-zero voltages, with both AC and DC. However, in the absence of a non-zero reading (negative, for under-reported results, positive for an over-reported one, in the case of DC) when a zero voltage was applied, this cannot really have been due to a fixed/constant offset error.
An offset error doesn't necessarily mean "zero reading for non-zero input", it can be the other way round. For DC you'd be likely to notice a negative reading for zero input, but for AC you wouldn't generally see a negative reading.
As you say, with DC there is no problem at all - if there is a fixed/constant offset error, then there will be a reading (positive or negative, as the case might be) with zero applied voltage. However, even when measuring AC, it is likely that one would, again, get a non-zero reading with zero applied voltage if their were a fixed/constant offset error (don't forget that most of the electronics will be working with DC, even for AC measurement).
I'm not sure what you are thinking would happen if their were a 'fixed/constant offset error' in an AC voltmeter ... say there was a fixed offset of exactly +10V. The closer the true applied voltage got to zero, the closer would the displayed voltage get to 10V. Even if the true voltage were, say, 0.00000001V, if the meter was up to it, it would display 10.00000001V - but are you suggesting that the reading would suddenly 'jump' from 10.00000001V to zero if the applied voltage was reduced from 0.00000001V to exactly zero? I think you are probably thinking about something more complex than a simple fixed/constant offset error.
Kind Regards, John