I do know what 'objective' and 'objectivity' are supposed to mean.
So that's not it.
Just take one of your arbitrary choices: "perceptible by a person".
Who would that be?
The DOF criteria were set using large panels of people, with the criterion they ended up 'defining' being some sort of statistical mean.
No other way. No 'objective', or even common, thingy in sight.
"The most important thing about DOF, by far, is that it is a perceptual thing. Not an 'autonomous' entity with an absolute dimension. (Despite all the formulae and calculators people like to let loose on it)."
A viewing distance may be measured 'objectively'.
But so that 'arbitrary choice' may be 'objective' (we can set up a thread about whether 'objective' is a meaningful concept at all. But another time perhaps ).
But we're not concerned about viewing distances, but with how an image looks (!) from that viewing distance.
Totally and utterly not objective.