Could the catchment area not be adjusted so that you were eligible to apply if you lived within a reasonable walking distance, say a mile, for example?
For many people that would automatically increase their choice of available places and places could simply be allocated on a lottery basis?
It might help with the house price issue.
I would still say children in care/siblings/SN children should be allocated places first however.
Having said that, I know some people would not be at all happy because it would mean they couldn't necessarily 'buy or lie' their way into the school of their choice and might end up in a school that isn't top of the league table, so to speak.
However, the impact of this might be positive on the education system as a whole, as the enthusiastic parents would be spread out evenly in the borough.
Initially, it wouldn't help folk like who me, who simply want their child to go the nearest school so they can be with their friends, but long term, if standards improve across the board, it could increase choice for us all.
Where children do not have any school within a mile of their home, then they ought to get first refusal of a place at the school at their nearest school.
Not perfect either, I know, but fairer surely?