Round here theres over 100 and they are all local authority owned and just operate the morning and evening services as well as being available for schools to book for trips or things like swimming lessons. Usually each bus only operates one school route (schools have 1-3 yellow routes with a couple as many as 5) though there are a small number where the bus can operate two different schools with staggered opening hours routes.
That's similar to how the Cheshire ones operate. The same bus always runs the same route. They are used on shorter school trips but if there is a school trip for an extended day e.g. returning at 5pm, then yellow buses aren't used and a local coach operator provides the vehicle for the school trip.
Theyve never been offered for faith school routes though some faiths schools have had a financial contribution toward bus passes based on historical agreements (like relocations and no other school available) these have all ended except for the poorest students.
The actual arrangement made between the C of E and Catholic churches and the government in the 1940s was that the councils would transport children free of charge to school if they didn't live within walking distance of a faith school and in exchange the church would fund building the schools and some of the upkeep. This was made in to a parliamentary act which hasn't been abolished. It was a very good deals for both parties, as you can imagine in the 1940s any promise of providing funding for buildings went down very well and the councils were responsible for local transport and they couldn't justify a faith school in every town so having a guarantee of a transport service went down very well with the churches.
Now in the recession most faith schools are better maintained than non-faith schools, so the council taking over the school building and maintenance works instead of providing free school transport is a cheaper option for them.
I dont think size is a problem really, their used on high school and sixth form college services.
In the case of Holmeswood Coaches they've taken what were built as 53 seater coaches consisting of a back row of 5 seats and 12 rows of 4 seats in 2+2 formation with an aisle and turned them in to 70 seater coaches still with a back row of 5 and 13 rows of 5 seats in a 3+2 formation with a very narrow aisle. (The aisle is narrower than the seats hence why the back row is still 5 seats and not 6.)
Like I said earlier I'm not convinced these are suitable for high schools with sixth forms due to the older pupils being adult sized. There's no way they should be used for bus services carrying only adults. They aren't even permitted to have passengers standing.