With this approach, already-running queries won't take into account the fact that new partitions have been added, but that seems at least tolerable and perhaps desirable.
Desirable, imho. No data added after a query starts would be visible.
If the COPY isn't trying to send any tuples to the now-detached partition, then it's fine, but if it is, then I have trouble seeing any behavior other than an error as sane, unless perhaps a new partition has been attached or created for that part of the key space.
Error in the COPY or in the DDL? COPY preferred. Somebody with insert rights shouldn't be able to prevent a table-owner level action. People normally drop partitions to save space, so it could be annoying if that was interrupted.
Supporting parallel query shouldn't make other cases more difficult from a behavioral perspective just to avoid the ERROR. The ERROR sounds annoying, but not sure how annoying avoiding it would be.
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Simon Riggs http://www.2ndQuadrant.com/ PostgreSQL Development, 24x7 Support, Remote DBA, Training & Services