In the past some primaries have actively sought to try and exclude DC with SEN from sitting SATS to 'massage' their results. There's been a crackdown on this recently so you may find it harder to get the school to agree. Hence the 'let him give it a go' reply, I imagine.
The whole SATS thing is hideous for schools and the DC. So much pressure is put on the DC and in some schools (certainly in my DS’s) all of Yr6 is just spent on endless SATS papers. There’s also a lot of pressure to attend before and after school SATS ‘booster’ sessions.
For anxious DC, it’s just hideous.
I was going to try and get my DS not to sit them but then I changed my mind for several reasons. While it is true that secondary schools get DC to sit their own assessments, as Thatsnotmycar says, the SATS data is used. Paradoxically, it’s in the primary school’s best interests to have a DC produce stellar results, but for a secondary school, if a DC’s SATS results aren’t great then in a good school, there’s more room for them to show improvement, IYSWIM.
Also, I felt that as my DS was going to be sitting many tests/exams throughout his life, he maybe should start gaining experience of what they’re like. However I do appreciate that 10/11 is very young to be sitting such formal tests so it’s a tricky one. In the end, my DS never got to sit them as they were cancelled due to Covid.
If your DS does sit them, he may be able to sit them in a separate room, be given extra time and have a scribe/reader. What has the Senco said? It's in a school's best interests to make as many adjustments as possible for DC.
As a slight aside, do you have a plan in place for when your DS starts secondary? You say he’s ‘so far behind’ and he has ‘TA support’. Does he have an EHCP?