Actually I have found with my three DCs at/were at a grammar school that once the stress of actually getting in is over, it has been fine.
They do work at a fast pace but I think it would have been much more stressful, for one of my DCs in particular, to have been always having to work because is lazy little gitto keep in the top sets at a comprehensive than actually doing barely the minimum at a GS, and still coming out with decent results.
Once they are in, the pressure is off to a certain degree. OK, if you want them to be top of the pile there, then it is going to be stressful but if you are just grateful they are there and are benefitting from a reasonably good education, then you can relax knowing they are going to pass their GCSEs, in a fairly well disciplined and ordered environment. If that's not for you, fine.
It depends how driven and ambitious the child or, in more cases, the parents are which leads to the stress. If they are very ambitious then that is the right environment for them, they will be encouraged and they will do well. However, my DCs were/are just happy to be at a school with virtually no bullying and with peers on the same wavelength as them.
Most children don't need excessive tutoring but do need to familiarise themselves with the test, as it is simply not fair that they are competing with other children who have been better prepared.