Would it not be possible to end up with a rather out of trim ...
well ... yes .. and no.
The reality is that, providing
(a) the stats are based on a reasonable and appropriate population
(b) the sample size in use is reasonable
the use of standard weights works out to be pretty close to the mark.
The above caveats relate to the following concerns ..
(a) it is very much a case of horses for courses. If the standard weights you propose to use relate to studies of relevant passengers, the weights will be OK .. ie, the standard weights appropriate to a plane load of little old church ladies out for a Sunday afternoon flight wouldn't suit a plane load of sumo wrestlers all that well ...)
(b) while there is variation in weight from passenger to passenger, this tends only to be significant for small numbers of passengers. Thus, use of standard weights on a six-seater tourer represents a much bigger problem than on a 747 .. as these variations tend to cancel out with the larger sample size. It is for this reason that sensible standard weights will be a little higher for smaller aircraft than larger so that the variation is less likely to catch the loading out unconservatively.
every piece of checked luggage is weighed at check-in anyway
.. but is that for loading calculations ? ... or excess baggage revenue ? On a less jocular note, transcribing a bunch of scale data on tight turnaround short haul flying can present a problem ..
Overall, use of standard weights does not present a problem .. providing that the basis for, and implementation of, those standard weights is appropriate.