I confess I am pro-SATS, speaking as the parent of a DS who got all 5's and another about to sit them who might get a 5 in Maths but may not even get a 4 in Literacy, despite a battalion of 'best efforts'!
I think it's a useful way of testing what's been learned, how well it's been taught; that the whole curriculum has been covered.
I may be older than some here but I can recall when it was perfectly possibly to go from 4-16 in school having been tested only the once, a failed 11+.
I don't think it's wrong to put a bit of pressure on a 10-11 year old, especially since it appears from a previous post on MN (about what a daft idea breaking education once, and once only between Y6-7 was, and being roundly told what a fantastic and completely logical break point this is...) that there's huge support for the change from possibly tiny primaries to vast comps- well, with a DS in Y8, welcome to a fair bit more pressure! Better they understand that from Day One, imo.
Yes, it's dreadful if your DC is anxiety wracked or a perfectionist, but I don't think abolishing the entire testing program for fear of upsetting these DCs is necessarily the answer, is it? Neither of my DSs were or are particularly stressed about them, even though Y6 is a bit of a SATS factory (in fact, DS2 is getting a bit of a confidence boost that though his English is rubbish, he's better at maths than he thought, and here's numerical proof!).
And, let's face it, the private school kids who end up in the most influential and best-paying jobs are tested from the age of at least 7, if not 4!
What shouldn't happen is for a school's SATS results to be available to anyone other than the parents, end of. League Tables should be banned.