I agree with you, J52. It's quite interesting looking at the profiles of Year 7 pupils. I've always worked in schools where CATs tests were administered plus a reading test (I think it was called DE). It's not uncommon to see uneven profiles and in the schools where I worked, pupils with very uneven profiles were given further test.
For example, a child with a very high reading score but average non-verbal score is often from a supportive family, which has encouraged reading, although the child is not inately that bright. Sometimes such a child will initially do well, but then tail off when higher level cognitive skills are needed. Conversely, a child with high CATs scores, but low reading, might have been underachieving for a variety of reason.
Children whose CATs scores didn't 'match' their SATs results were often retested. It could have been that they came from primary schools which spoonfed for the SATs tests for their own league tables. We knew which schools did that, which is why we preferred CATs to SATs.
Until the 1970s and 1980s it wasn't uncommon for specific learning difficulties not to be recognised.