I've only experience at Primary, where I'm a governor, but schools set their own admissions criteria so some may prioritise sibling link (most do), others won't (but I've never actually known a school that doesn't have sibling link as one of the top criteria). Normally children who are in care are top priority, regardless of any issues of faith or location. In the case of our school, we have been known to have to consult various sources when we have got to the stage of deciding which of two addresses is closer to the school, but generally speaking, the admissions decisions are all very clear cut, and are easy to work out according to the strict and published admissions criteria. The council are responsible for gathering and administering the applications and then the governing body are responsible for allocating the places. As governors, we don't know which of the applications have requested our school as a first choice/second choice etc. This has always galled me because given the choice, I would rather accept children who had expressed a strong preference to attend our school rather than wanted it as a second or third best option, but ultimately there are criteria, and having the criteria in place ensures fairness. After the offers have been allocated there is generally a frustrating and for parents, stressful stage of movement as parents reject their place in favour of another.
On the issue of it not being fair for faith schools to insist on church attendance, or for people who don't subscribe to a faith having less of a chance of getting a place, the church provide a huge chunk of cash to run the school, and so in return will prioritise families who support the church, via regular attendance. I hear a lot about about there being a legal requirement for faith schools to allocate a proportion of places to non faith children, but I've never come across this in practice. We have a number of non faith children in our church school, who are not regular church goers, but this is only because there was availability of places after all the faith based applications had been given places.
I'm not sure there is a better system really but it is certainly sophisticated enough to not be manipulated by people who cite reasons such as commute time. I know the LA just get frustrated with forms such as these because they end up wasting a lot of time as the parent inevitably is unhappy with the place they are allocated and want to go the road of appeals etc.