Developed and Emerging Markets Banks Convergence?

I think that the business model of emerging market banks has historically been collecting deposits and investing them in foreign sovereign debt (and not lending to local business except large and/or politically connected enterprises). Are we moving to the same structure in the rest of the world? At the same time the emerging markets are moving towards actual commercial lending? And, if so, does this suggest that investments as substitution for debt will become possible in the U.S.?