Fair point but I can think of at least two possible explanations.
Performance wise I think it's always a goal to use as little bleed air as possible i.e. lower demand on the packs. Therefore the less conditioned air that needs to be supplied to any system, the better SFC.
Maybe redundancy and system separation has been another factor in the design? Smoke QRH drill comes to mind where you can alternate between normal cooling and alternate aircond cooling by overriding fans (as you mention yourself). It is easier to identify aircond/equipment smoke if systems are separate (e.g. cabin crew senses smoke, but not visible in cockpit will indicate aircond affected)
A quick look at the Boeing suggests (if I read correctly) that indeed aircond air is used to cool the equipment. Any Boeing-thoughts on why the different designs?