Let me try putting it this way. Take four hypothetical children. All from the same state school, all equally bright, all score the same on their 11+ paper.
Child A - a year before 11+ day, Dad dies. Until then, had been well suported by motivated, engaged parents, but since the death the remaining parent hasn't coped well and hasn't give as much support as she would have done otherwise. Family is ok financially thanks to insurance polices and pension payouts.
Child B - a year before 11+ day, parents separated. The split was amicable and child B sees the NRP regularly, and both parents are supportive of education. The RP went on benefits temporarily so was eligible for FSMs, but now has a job and no longer gets FSMs.
Child C - from a traveller family. Both parents have low levels of literacy, and numeracy but want their child to do well and have ensured that their child is at school every day and has done what they can to help their child's education, although that has been very little.
Child D - from a family with a fairly low income because of a siblings disability, but not low enough to qualify for FSMs as one parent works full time. Home life is a struggle because of the needs of the disabled child and Child D sometimes has to help with caring or household things.
So, is it really fair that child B is allowed to get a lower score on test day thereby getting a much sought after place at the grammar school when the other three miss out because they are expected to get a higher score?
I realise this exact situation is unlikely, but if this is what schools are doing then the fact is that there will be children in difficult situations who don't get offered places in favour of FSM children who could easily be better off overall. And I just don't think rules enforced by government organisation should be doing that.
It might cost more money and effort to provide tutoring for all that want it, but it has to be a better way than fiddling with results.