OK, OP, here's a thought experiment - something pretty much exactly like this happened to my parents' NDNs, in their small village:
So I let's say I live next to St Joseph's RC Primary. I'm an atheist but not overly fussed whether my dc go to a faith school or not - I just want them to go to their local school.
You live 3 miles away, in the next village. Your house is next to Anyvillage Community Primary, which is non-denominational (but will still be obliged to have 'broadly Xtian assemblies' etc).
St Joe's is excellent, & over-subscribed, & your eldest can have a priority place & travel 3 miles to it. My eldest doesn't get in as a result of you & other RC parents wanting the place. For the next two years you & I pass each other every day on the school run as I drive 3 miles to Anyvillage - which is just as good a school but less desirable to me because of the travelling.
Two years later, St Joe's isn't looking nearly so attractive. The HT has left, say, & the new one's a basket case. You decide to move your eldest to Anyvillage & to send your younger child there, too, when he reaches school age. OK, they'll not be at a faith school, which is important to you, but on balance you're just not happy with things at St Joe's, & Anyvillage is on your doorstep, so that's a bonus.
I apply to send my younger kid to Anyvillage too, so he'll be with his brother. Because I'm 3 miles away & you (& the other RC parents in Anyvillage) don't fancy St Joe's anymore, he doesn't get a place. He'll be going to St Joe's. I'll have to drop him off at the Breakfast Club each day before taking his elder brother to Anyvillage, unless I decide to uproot the elder one from the good school he's happy in & send him to failing St Joe's, too.
Basically: you get two choices at every stage. I get the choice you don't want. How is this a fair way of doing things?