I don't think there's anything wrong with grammar schools themselves, but the trouble with the system is that it wrote off a while load of other children at age 11, and certainly the old secondary moderns were very much seen as lesser by a lot of people- and some of those attitudes can be seen on this thread about comprehensives in grammar area's.
We still haven't got that sorted - there have been constant changes to try and cater for less academic children, especially now most are expected to be in education until 18 - BTECs, T-levels, apprenticeships. Obviously nothing will suit every child, as no two people are the same, but there is much more focus on academic education (which is also important, but not everyone is academic.)
Private schools can be selective, and the top schools are fiercely so. There is hierarchy in the private sector - when I heard where my godmothers boys were going, I had to bite my tongue and not say, "aren't they bright enough for somewhere better?" You also get hierarchy in the state sector, where there are big enough populations - certainly of the secondary schools in my town, some are more academic than others (but in my home town, there is only one secondary, with a large rural catchment.)
But what is really important, what we should aim for with all children, is they get a good grounding in a range of subjects. Some children are all-rounders, others are clearly artists, linguists, scientists, sportspeople. No one can known if they might have talent in music or hurdles or biology or French or poetry or whatever else if they simply don't get any exposure to these things. Having English and Maths are the foundation of most other subjects, the gateway in, but we need breadth as well as depth - we should be using them to unlock other things.
I went to a comprehensive state school, and in my days, I got to try different languages (Latin to A-level,) I tried many different sports, I tried art in different media, I was exposed to different styles of music and had free violin lessons. I did maths and science. Other people stayed on in 6th form doing extra numeracy and literacy, so we weren't only catering for the academic ones. I learnt all sorts of things - and I was entirely state educated. It's how education ought to be, and we are failing if we can't offer it like that. Not everyone will end up musical or artistic or as linguists or scientists, but they should all be learning these things exist and be given the opportunity to try them, to find out where their strengths lie.
But if schools aren't offering all that, then places like Tit Hall have to go where those with the entry requirements will be found.