It is a little surprising how Manchester - Leeds gets four trains per hour but Manchester to Britain's second city gets only two!
Agreed
Five trains an hour from Manchester to Leeds at the moment (plus three via Rochdale that are all obviously overtaken enroute) - with a sixth on the Huddersfield route planned before long (admittedly replacing the Manchester - Huddersfield stopper, but will be a sixth train an hour from Manchester to Leeds).
I don't know why Manchester - Birmingham has been so badly treated over the years - only around seventy five miles apart (further, obviously, than Manchester to Leeds, but still ought to be "commuter" territory).
Maybe one reason for the neglect is that Manchester and Leeds are often tied together in a "Northern Powerhouse" kind of way (Osbourne's Powerhouse being just the latest version of plans to link cities "oop north" together - e.g. Prescott's Northern Way -
https://en.wikipedia.org/wiki/The_Northern_Way - am sure it won't be long until Corbyn comes up with some grand scheme of his own...).
Whereas Manchester to Birmingham links different English regions, so doesn't have a "champion"? Dunno.
HS2 will significantly improve things - bringing the journey time down to 42m between the cities - compared to roughly 1h30 today - but that shouldn't be an excuse not to improve things between Manchester and Birmingham sooner.
There are talks of linking the current Manchester - Stoke "stopper" further south, though that won't improve "end to end" journeys - its a step in the right direction at least. Otherwise, this is a seriously neglected market - a half hourly Voyager is a poor offering.
(also, on the subject of poor Birmingham links - Leicester has a terrible link to the West Midlands - given the size of them and the fact that they are only around thirty five miles apart)