I don't think that standards of education are higher in grammar schools.
I went to one as a kid in the noughties. Had many amazing teachers and many crap teachers who phoned it in because they could get away with doing so. They chucked out a third of the year after Year 11 for not getting good enough GCSE results and replaced them with high-performing kids from local private and comprehensive schools. Pastoral care was rubbish. Anyone who struggled academically was told they weren't trying hard enough (and sometimes humiliated, eg through results in tests being openly shared with the class in a failed effort or somehow motivate low performers through embarrasssment).
I also used to teach in a grammar school. Same impressions. We had several kids joining our sixth form from local comprehensives who told me that they felt the standard of teaching and rigour was actually worse at the grammar school and they regretted making the move.
On top of all that, I know several very bright people who went to grammar in the 60s or 70s in the days of the 11 plus. Some excelled. Some did badly and had their confidence totally shattered. This was especially true of kids from working class backgrounds who had been top of the class at primary and then ended up getting shamed and labelled as stupid in a grammar school setting. These are bright and curious and motivated people by the way who have found their niches as adults but they left school feeling stupid.
In contrast there are some non-selective schools now that achieve amazing results and get more kids into Oxbridge and other top unis than many grammars.
Yes, there are fewer behavioural problems in a grammar school because the kids who attend tend to skew more towards being good at achieving within the structure of the curriculum (which in turn helps to encourage kids to feel there is a point to listening and working hard), and also tend to have more parental support and discipline (so they have help to do their homework and encouragement to listen to their teachers and sometimes tutors on the side too). It isn't the school that helps the kids so much as the kids and their parents who help the school. Historically grammars have been dominated by middle class kids and by kids from a working class background but whose parents are very pro-education. More grammars are changing this now, for example by prioritising free school meal kids in their admissions criteria, but I suspect the overall pattern remains the same.
I won't deny that I'm glad I went to a grammar school personally. I'm the sort of geeky kid who got bullied in primary school and I appreciated the quieter environment in a grammar that helped me to focus and learn. There were also kids at my school for whom a grammar was a chance to get where they wanted to in life and perhaps they wouldn't all have achieved as highly in a comprehensive. I don't want to pull the ladder up behind me and my friends.
At the same time, I find it hard to see how grammars are the solution to improving education either. Nor does it make sense to me to label kids at 10 as 'talented in the arts' or 'talented at sport' and sort of siphon them off / hot-house them that way either. For one thing, the model won't work at all in low population density areas. For another, it just labels kids too early and doesn't take account of how kids can develop and shine at different rates in all areas: sport, arts and academics.