You can't do much to improve a school when the raison d'etre is essential We Are Here For the Kids Who Couldn't Pass The Test. The whole place is likely to stink of failure, the expectations will be low, and the school will struggle to find and retain good teachers.
Comps with sets avoid the above problem to a large extent, as there is the potential to move up/down sets (which gives hope to those who are slower to mature, while also ensuring that those who are higher achievers don't just "relax" and take their status for granted...potentially an issue with those who pass the 11-plus).
Sets also ensure that a kid who is (say) poor at maths but great at languages can be in classes which reflect their abilities--in an 11-plus system, such a child will inevitably be in the "wrong" classes for some of their subjects.
Finally, children in comps can all benefit from the same quality of teachers, whereas in 11-plus systems, secondary moderns get worse teachers than grammar schools, as teachers with the best teaching skills and most experience understandably prefer to teach in the grammar school.
All these reasons are why parents in most parts of the UK demanded an end to the 11-plus system, which is why Thatcher as Ed Secretary was forced to comprehensivize the system across most of the UK. She didn't want to, but parents demanded it, because the 11-plus system is, and was, shite.
I'd like the remaining ones to go. Perhaps by stealth - require the GSs to take on an ever-growing % of FSM pupils until the difference between them and the SMs effectively ceases to matter.