@SussexMumofOne beware of marketing....there are plenty of girls at TGS with MH issues, just as there are at TWGGS and WOK. I have friends with children in all of the mentioned schools and there are issues with them all, and the levels of support given - you need to choose the school that suits your child best, and talk to existing parents if you can. Yes, they all have pastoral leads and say they deal with things robustly - but it's different once you are in the schools themselves, and obviously every child is different.
(All four of mine have been or are currently at west Kent grammars. The head at Skinners' does try to stop parents parking - they pay no attention to the constant pleas not to park like idiots and to use the free car park - it's the same at TWGGS and TGS - in fact any school really.
With regards to the OP's question - having priority for local children was partly driven by funding - it costs KCC a fortune each year to facilitate the 11+ testing, many of the candidates are OOC with no chance of getting in, and the schools are asking for funding for buildings etc - so KCC made some of their capital contributions dependent on taking a larger % of local children so that local council tax payers benefit.....(I'm not saying I agree - that's the argument they have put forward).
The traffic in and out of Tunbridge Wells in the mornings and evenings is horrific, so I guess they want to reduce congestion, allow local children to walk to school and have local friendships. When DS1 started at Skinners' there were children coming from London and the south coast - they were exhausted by their commutes, and couldn't do stuff at the weekends, or be part of the school community in the same way. It's been lovely for his brothers to have friends they can get to on a bus or walk to easily.....