I think that informal monitoring of children's learning is a must, with that information transferred either in writing or personally from one teacher to the next year's teacher.
SATS however, are in my view a heap of shite. Lower achieving schools panic about them and waste/ misdirect huge amounts of resources into not appearing to be doing badly, and schools at the top of the charts are frequently playing fast and loose with rules and regulations governing them (read- cheating) to keep their top spot. They were never meant to test individual children, but to keeps tabs on the school; however, most schools are using the information gained to assess children.
I think testing at yr R-4 should be done informally but properly. If problems are apparent with literacy at beginning y4, children should be scooted into a "high dependency" unit with more staffing, more fun (!), assessed extensively, and assisted to gain literacy in the quickest possible time period. If they catch up, they can go back into standard classroom as and when they are ready. If there are still major problems at 11, they should have the option of delaying entry to secondary school until they are 12 or 13- if they go into sec school unable to read or write, they are basically stuffed.
By extension, I would scrap y6 sats on the premise that they are pretty damn useless anyway other than to highlight the lack of proactivity of the school over the previous 6 years. If a child can read & write and do basic maths, brilliant. If they can't, it's too bloody late by then.
Yr 9 SATS in the main only show the same gaps in attainment as the yr6 ones, and are another nail in the coffin of those who left primary school illiterate or functionally illiterate. Not very motivating. They should be replaced by intensive careers advice at yr9, and orientation according to desire and ability thereafter.
So basically, scrap the bloody lot of them is my answer.