This proposal seems like it would run aground on the actual complexity and changeability of river systems. The River Great Ouse, to take an example that's local to me, runs in four channels between Earith and its outflow at Kings Lynn (the Old and New Bedford Rivers, the Great Ouse proper, and an unnamed flood relief channel). But this is a relatively recent configuration: the Great Ouse formerly turned west at Littleport (rather than north as at present), reaching a confluence with the River Nene before flowing into the Wash at Wisbech, while the Little Ouse flowed north to Kings Lynn.