Lowclouds,
I have taught in a 3 tier system in a rural area.
In that scenario, it works well. Small, village-based First schools (to Y4). Ideal for first few years at school - no transport to negotiate as a 4 year old, 'family' atmosphere, typically mixed year classes.
Then fewer, larger, middle schools, usually in the slightly larger centres of population (Years 5-7). Ideal for children old enough to get buses, benefiting from larger peer groups, more specialist teachers (taught on a secondary model of subject teachers in general) and concentrating resources such as sports facilities in fewer, larger centres.
Finally a small number of upper / high schools, children bussed up to 10 miles. Ideal for older teens, all with 6th forms.
[I have also taught in R-5, 6-8, Year 9+ 3 tier - I prefer the R-4 version as I think by year 5 many of the small First schools cramp the style of upper KS2)
It doesn't matcgh key stages, but it does seem to match 'developmental stages' of children - small child, older child, teen.