The only people who benefit from good Sats results long term are the schools. The stressed-out children gain nothing - but can take ages to get over their fear of tests and feeling of being a failure.
AFAIK most secondaries do another load of tests in the first term to decide sets for maths (they often don't set for anything else till much later), and even if your DS ends up at a school where the initial set allocation is done based on Sats results, they are always flexible about moving people around later.
In your position I would encourage your DS to resist the pressure, and don't make him do extra work at home. Then smile politely and nod at the teacher when she tells you how many practice papers he should be doing, and let him go and play football or whatever instead.
Year 6 was a wasted year for my DS as his school also started drilling them for Sats at this stage, and did nothing academic after Sats finished. He was bored to tears and frustrated by the lack of anything new being taught all year.
FWIW, he is on the G&T register at his new selective secondary, and is doing brilliantly at English among other things, but (only) got a 4 in English for his Sats - I think his atrocious handwriting may have had something to do with it. He also only just scraped a 5 in science but got 90% in a yr 8 test last week (top of the class).
IMO Sats don't tell you anything except how well children have been trained to jump through a particular set of hoops - completely worthless and irrelevant to everyone except the compilers of league tables.