Come and tell me some of the benefits for children in going to a grammar school

I think you need to look at the actual schools in your area.

My experience (from my mother) is of a hugely inflated sense of self importance.

Would dd thrive in a grammar, or a comp?

at mumble's MC white comment.

I went to a white WC catchment school. Looking back, I don't feel that the experience made me a more rounded person. Also, its like saying that our relatively affluent children can't understand what it's like to be a poor African kid because our DCs don't go to a school with such children.

Anyway, we chose a selective education for DS because we noticed at primary that he only does enough to be on the top table. Most kids would get 7 out of 10 for spelling for example. He didn't see the point in aiming for 10/10. Getting 8 or 9 was good enough. So why spend 15 min on revising when 10 min would get him a result that he was happy with, was his thinking

At his selective he has kids that are cleverer than him and this pushes him to work harder

Anyone who struggles gets extra help

Dds is very mixed race, and very mixed affluence. Her primary had one mixed race family

Far far less disruption and distraction as no boys to show off to

The principle is that the teaching can be targeted at your DD's ability, or at least closer to it than at a non-selective school. So teachers don't have a full range of capabilities to deal with, which reduces one challenge for them and enables them to teach better. For example they can then stretch the brightest further, and support the "lowest" ability kids better where in another school they might be average ability and not given any extra assistance.

DS is at grammar (Upper Sixth) and has been there since yr 7. It hasn't been a great experience for him but I'd say these are the pros and cons:

Pros:
It is expected that you will excell academically and that in itself may be a good thing.
You get the same facilities as at a private school, or better. Eg at DS's school there are national-level rowing, fencing and equestrian teams.
No-one is allowed to fall between the cracks academically. If you get a B, you will be expected to do better.

Cons:
The pressure is intense. DS unfortunately got a bit fed up of it and it had the result of him caring less, not more.
The cohort certainly at DS's school is 98% white, "generally very affluent" - Ofsted, middle class types. Many children here live in homes with pools, tennis courts etc, which in my view leads to them having no clue about how the other half live.
The teachers are under such pressure to provide results that pastoral care can be very very poor.

I'd say it depends on your child and whether they are quite robust as well as academically extremely able.

I'm not sure you can bunch all grammar schools together and call them 'good'... and not all children 'fit' the mould that thrives in a grammar school environment. You may have a child that is academically capable of passing the 11+ and gaining a place, but the particular school may not be the best all round for him/her.
My DS went to a super selective grammar, and it was superb. Academic results aside, (and actually, my son under achieved at GCSE at this school), the pastoral care was exceptional, the opportunity to compete in sport was fantastic and the house system ensured a very close and cohesive student body. But there were other boys at the school who clearly didn't enjoy that same experience and would have been better off at a different school.
My DD has not gone to a grammar and is taking her GCSEs this summer. I suspect her results will exceed her older brother's, without the hothouse environment that you get at a grammar school. It's horses for courses really.
I'd go and have a look at all the options in your area and then take a view as to whether it is worth going for it.

Because they are better schools, and your DC will get a better education.