I think it is impossible to decide this based on Chapter 1 alone, for the second criterion (qualitative correspondence with common sense) is not yet specified formally.

If you look into Chapter 2, the derivation of the product rule, he uses this rubber-assumption to get the results he aims for (very similarly to you).

I think one should not take some statements of the author like ("... our search for desiderata is at an end... ") too seriously.

In some sense this informative approach is defensible, from another perspective it definitely looks quite pretentious.