I see contradiction in:

1) The AGPL is philosophically well founded, the GPL is arbitrary.

2) The AGPL enforces an arbitrary distinction, the GPL does not.

I think I've found the confusion. I was still talking about the GPL in my second comment. I see why that was confusing given that you'd explicitly added the AGPL into the discussion, sorry.

I might have better stated it as "I agree the AGPL removes the tension, I think the AGPL is philosophically coherent. But the FSF still primarily pushes the GPL. [transclude prior comment]"

Hm, I still don't see how that resolves it.

You say "How, and where, can you draw the line between those things?", when the AGPL does precisely that and the GPL refuses to.

I'm not trying to criticize, here, I'm trying to understand...

I'm criticizing the GPL as inconsistent because it draws lines haphazardously. That it is ok with the API but not with the distribution feels arbitrary and inconsistent to me.

The AGPL is elegantly precise - anything you do to the code becomes public.

The bad is elegantly precise - anything you do is fine.

GPL is complicated and inelegant - some things are fine while their near equivalent actions aren't.

Edited to clarify

"Anything you do becomes public" is an inaccurate description of the AGPL. That consultant can keep things private.