I have 2 children at state grammar in Birmingham where 4,500 take exams for 600 places at 5 grammar schools. Many of the 15,000 children in Birmingham who move to secondary each year opt out of taking test and quite a few from surrounding counties take Foundation exam. There is no catchment area so I suppose these schools are classed as super selectives.
Don't believe everything you hear about the amount of tutoring (paid for and DIY) that children do. I think some people like to exaggerate to show their children in a good light, that they should be in such a school because they like studying. I also believe it is what the parents want for their children rather than what the children want in some cases.
If your child is near or at the top of the year, enjoys learning and will succeed in an environment where children want to learn, move along at a good pace, happy to do nightly homework, then preparing them for the 11+ is an option. it isn't just about passing a one-off exam, it is about 7 years of their lives in such an environment.
Some areas of the country have grammars that take the top 25% whilst others take the top 5%. The amount and type of preparation depends on your child, what you and your child want over the next several years, the school(s) you are applying for, the county it is in and the competition for places. Although some of the members of the forum are quite intense, I would suggest you view www.elvenplusexams.co.uk for more information about the schools you might want to apply for, have a chat with your child and visit the schools to see for yourself and to motivate your child.
Although SAT levels are an indicator of the ability of your child, the 11+ is very different and tests potential rather than what children have learnt and remembered. I know of supposed level 6 children who didn't get into grammar schools and some level 4s who have. One doesn't know how your child will perform on the day - the elevenplus website forum is littered with examples of very bright children whose parents have been through a very traumatic appeal process to demonstrate their child's level of ability, because they didn't perform to the level expected of them on the 11+ exam day.
Please do your research and if it is something you and your child want to attempt, then put in place a realistic plan to prepare for it, including allowing plenty of time (9 months to a year at the most), understanding what your child should know, practice papers, a mock exam to get them used to exam conditions, time away from studying, paperwork to be completed for the school and the county authority and the timescales associated with this. If it takes several hours of extra study each week, perhaps it is not for your child. Many children who don't get into grammars as they didn't score highly enough or didn't take the 11+ do very well.
I hope this is useful and good luck.