I think the English system is very confusing. Whilst it's not perfect here in Scotland, it definitely does seem easier & dare I say it, fairer to get your kids into the local school.
Here (Scotland), every school non-denominational (ND) & catholic (RC) has a catchment area. In effect, this means every household has 2 catchment schools.
Priority is given to kids in the catchment area with sibblings at the school followed by catchment kids without sibblings. Next it's kids outwith the catchment area with sibblings already at the school & last is outwith catchment with no sibblings. Distance from house to school would come into effect if the school was over subscribed.
For the RC schools baptised catholics within the catchment area are the first priority and then it's the same priority system as ND schools.
To summarise, catholic kids are more or less guaranteed a place at their catchment RC school, as are non-catholic with sibblings. Often, non-catholics without sibblings are refused entry to RC schools if there is high demand. However, as far as I'm aware, all kids within the catchment area are guaranteed a place at their local ND school.
If parents do their homework before buying / renting a house, ensuring their home is in the catchment area of their desired school, they're unlikely to be disappointed when it's time to enroll their child into primary education. The main problem here is when parents try to place their kids in schools outwith their catchment area, especially if it's an over subscribed school.