@chocolatefiends I think it's a terrible idea if you want your child to be happy and settled in school in year 7.
The purpose of SATS is, I think, to ensure that the school is teaching them well before they go to Secondary school and to ensure they know what they need in basic subjects. They are not assessing the child. However the fact they exist means that the children who are not at a good level gets lots of extra help and focus from school to improve their standards before they get to secondary school - which has got to be good for the children.
Yes, pupils can get a bit bored of sitting practice papers in year 6. But they don't need to get stressed about them - such stress usually comes from the parents. The fact that you are making such a big deal about them when your child is year 5 (or below) is quite worrying.
My DC got the best, focussed, education of their primary school in year 6 - the school put some of the best, most experienced, teachers in that yeargroup to make sure that all the DC got the best education possible before they left the school and went onto secondary.
If you take them out of school for this reason in year 6 then their friends won't understand why. It puts their friends' parents in a difficult position and they probably won't explain to their children that you are choosing for your children not to sit SATS, and so these families could easily disassociate from you.
It is unreasonable to assume that they will just slot back into these friendship groups in year 7.
Year 6 has so many fun things - school trips, school plays, extra sports etc when the curriculum is finished. There is also PSHE, science, prep for transfer to secondary etc. It is also reasonable for children in year 6 to be a bit unsettled right now as they know they are going to move on from their cosy primary school in a few months and possibly go different ways to many of their current friends - and that is nothing to do with SATS.
Children can also do things outside of school - I assume your DC have hobbies/extra curricular clubs which will take their mind off school?
You do also need to check whether current primary is a feeder to the secondary before you remove your child from it!
If your child was being bullied and it couldn't be dealt with, then that I could see why you might take them out of school until a better solution was found. But not that you don't want them to do some hard work improving their knowledge ready for secondary school and then sit a few tests.