Dear Philippe,
I think -- and I am only half-remembering this -- that oxidation is autocatalytic (oxidation products speed further oxidation), so rinsing with used/oxidized developer will speed oxidation of fresh. As I say, I'm not sure, and it may not be for all developers. Even if it does happen, I don;t know how important it is. I throw this in because someone with more knowledge than I may be able to confirm or refute it. Certes, I'd prefer a water wash to a developer wash.
Cheers,
R.