I cannot see why we cannot do both? You could have the Core protocol serving as the settlement layer and a side chain doing the Payment network. We already have off-chain service providers doing a

good job at handling the payment side. { Or a combinations of them } We should look at this from more sides and have a three dimensional  view on this topic .... Bitcoin are adaptable with Side chains

to handle several functions.  ... SegWit will address some of the capacity issues and the rest will fall in place after that.