]For that matter, why divide the Midlands in two? Any reason other than size?
Well there are linguistic, historical and cultural differences (even landscape ones come to think of it), but the main thing is functional geography. The West Midlands is dominated by a single large conurbation (that in turn is dominated by Birmingham), while in the East Midlands there is no dominant city. Of course the East Midlands is complicated by the fact that a fairly substantial part of it (i.e. Lincolnshire) is not really part of the Midlands but has nowhere else to go.
If York is a separate region rather than part of a monolithic North England, then why couldn't all of Lincolnshire be part of Greater York instead of merely the Humberside? Or alternatively, why would it be a bad fit to be attached to East Anglia?