But the next Chesham departure "After 09:10" is at 09:34 - when
Off-Peak applies to fares, anyway.

Am I missing something?

It allows people through the barriers rather than blocking the rather restricted booking hall. Although that does assume that people will be more concerned about the cap rather than the headline fare which I doubt.

What possible objection would there be to an additional train at 0914,
for Oyster users?

Remember that the Chesham branch is single track and can only accomodate 2tph in each direction.

IIRC the times are determined by Chiltern wishing to avoid overcrowding on one of their "peak shoulder" services.