My son is in yr9 at QE. There are a lot of 'myths' surrounding the school, which are best addressed by visiting yourself and making your mind up.
With regards sixth form admittance it is based on internal tests taken throughout year 10 & 11, not on GCSE results, so there is no 'last minute.com'. Parents & boys are very aware of the system and offers for A levels are made very early. I would say if you want your son to attend a school where he can guarantee carrying on into sixth form from yr11, QE might not be the school for you. The sixth form is seen as quite distinct & separate from the lower school. We took the view that the education he would receive from 11 through to 16, with excellent GCSE results, would set him up to take his A levels wherever he wanted (he has always thought he would like to attend a co-ed sixth form). All sixth forms have admittance requirements, my DD is at our local comprehensive where the admittance to sixth form has changed this year, requiring much higher GCSE grades. It really will be a panic in August if she doesn't meet these requirements. DD will probably be 'excluded' from taking various A levels, due to not meeting various requirements, such as A level Psychology, which the school now require GCSE grade 6 Maths.
A proportion of boys that leave at the end of year 11 do so by choice, for many reasons. They move to independent schools where they are offered scholarships, to co ed, other grammar schools nearer their homes, for example. It is incorrect to say that every boy that leaves at the end of yr 11, is 'forced' out.
With regards to the entrance exam, again I think there are a lot of myths surrounding this also. Yes, nearly 2000 boys take the exam, but many take it as a free 'mock' for other school entrance exams and have no intention of applying to the school. Most boys apply to multiple schools, including the independent schools and even if they score highly on the QE exam, take up a place elsewhere. It is a school without a catchment, attracting many eleven plus 'tourists'. There are 180 places in yr7 and I believe the school goes down to about candidate 300/350 to fill those places. Yes, you do have to be very good at Maths & English to do well in the exam, but my DS always maintained it was being able to work accurately, with speed, which was more important, as many boys didn't finish the papers. As teachers, we prepared DS ourselves, going through eleven plus papers and covering the yr6 syllabus, for about 5 months before the exam. QE was his choice.
Every child is different and school experiences are so subjective. DS has not found QE to be a 'hot house'. He has no more homework than his peers at other schools, he has made great friends and is very happy at his school. He is also receiving an excellent education.