Well, clearly you're not bothered because your child is at that school. Presumably you prefer that school to the comp, it seems in some way better to you? Maybe the parents of children who get FSM would also like to access your school? And go to university? And get good jobs? And the obvious institutionalised discrimination doesn't bother you?
The only reason I prefer the grammar school in my area for my DS is that its general level of teaching is at a more advanced level, and there are more kids there with similar attitudes to learning and knowledge as him, so it provides a more appropriate education FOR HIM.
If the school were appropriate for a child on FSM then they would be there (as a few are) because they would have passed the 11+. (I'm in a fully selective area so they take 25% not 1%, and plenty of kids here pass 11+ without tutoring.)
But what your post overlooks, and what always seems to be overlooked, is that the non-grammar schools here (as everywhere) get THE SAME money from the government, have access to all the same stuff, to facilities that are just as good (actually probably better in our case - DS's school is really falling down). And actually now with the pupil premium, most secondary moderns will presumably get MORE money than the grammars down the road.
There's this bizarre idea that grammar schools get some kind of special privileged deal that gives their kids an unfair advantage, which has no basis in reality. The only thing they have is different kids.
That's what I meant about treating the symptom. I suspect people dislike grammar schools because they make the different educational levels of kids at 11, and the different family backgrounds behind them, OBVIOUS. But a kid going to school with no breakfast and no motivation is still going to be playing up in the bottom set at a comprehensive school. The presence of the other kids there who are academically able and motivated and supported isn't going to magically "save" them.
If you want to do something about the disadvantages that put them in that position in the first place, then I'm all ears. I've voted Labour all my life and am more than happy to pay the taxes necessary to address those things. But making sure everyone goes to comprehensives large enough to hide the problem, isn't doing anything of the sort.