Trafford has grammar schools whereas Cheshire has comprehensives, so there is a lot of cross boundary travel. Bright Cheshire kids go to Altrincham Grammar School for Boys, Altrincham Grammar School for Girls, the Loreto Grammar School or St Ambrose College (Hale is the nearest station to the first two), while many less bright kids from the Altrincham/Hale area go to Knutsford Academy rather than the Altrincham secondary modern schools.
It gets slightly complicated here. The Catholic primary in Knutsford is St Vincents, which is one of the feeder schools into St Nicholas High in Hartford, so all Catholic pupils at St Vincents in Knutsford automatically get offered a place at St Nicholas. Cheshire school children do not, by default, do any tests which determine which high school they can go to. Although, that doesn't prevent their parents applying to a grammar school and arranging for them to do a test, arranged by the school they are applying to. Bright pupils tend to get good GCSE results at St Nicholas, they have had pupils get 11 GCSEs all at grades A* & A or 7-9, so it's questionable what the advantages are of sending children to Loreto or St Ambrose instead. The possible exception is the St Vincents pupils who live in the villages around Knutsford e.g. Mobberley, which are closer to Hale Barns than Mobberley.
The parents of the children from Trafford who don't get into grammar schools may prefer Knutsford over the secondary modern but the reality is the secondary modern schools in Trafford don't have enough places for all Trafford schoolchildren so some are always going to have to travel, even if none of the parents from Trafford didn't wanted to send their children to Knutsford.
For the large flows it's debatable whether it would be better to have school buses rather than the pupils using the train. However, for villages like Ashley and Plumley, it doesn't really make sense to send buses for so few pupils when there should be a train service running to at least an hourly frequency.
The other thing to consider is there are always one or two not going to their most local school. For instance, I'm aware of Knutsford Academy being unable to offer places to children who move to Knutsford and try to join part way through their secondary education, which can result in Knutsford pupils going to Wilmslow High and Rudheath Academy, while Altrincham pupils of the same age are attending Knutsford Academy. In instances like these it's again easier to put these pupils on existing public transport where possible.
Really as Northern are supposed to be providing a service which caters for essential journeys within government guidelines, they should be ensuring their services cater for all school flows from 8 March.