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. 
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. Exactly, that is what I`m talking about exactly.
The CORE protocol is the settlement layer.
And the offchain entities built on it serve the unique purposes.
It's purpose orientedness or how you call it. But the core protocol is settlement layer, that is crucial.