English exams in particular were hit by delays in marking
Essay questions in Sats tests are "subjective and stressful to mark" and should be replaced, a report suggests.
The Centre for Policy Studies think tank says multiple choice questions are a more accurate way of testing.
Essays written by students in England nowadays are often "virtually unintelligible" with even basic errors not being corrected, its author said.
But the Department for Children, Schools and Families said it was important to test writing skills.
Tom Burkard's report for the right-leaning think tank says replacing essays with multiple choice questions would save a lot of money in an exam system which costs £700m per year to run.
Mr Burkard said recent marking shambles had undermined the value of the system.
Sats for 14-year-olds were scrapped after last summer's problems meant long delays in schools' receiving marks, but 11-year-olds in England still sit them in English, maths and science.
English papers were the most delayed as the essays take longer to mark than answers in other subjects, which are more likely to be simply right or wrong.
Mr Burkard says the current problems in marking Sats are systemic, and that repeated marking failures are undermining the reputation of the testing regime.
It is impossible to find enough good exam markers to grade 600,000 Sats essays, he told BBC Radio 4's Today programme.
"And you have to bear in mind that the kind of essays being written by today's pupils are virtually unintelligible.
"To suggest practice makes perfect when they are writing papers which are virtual gibberish is a great error."
Modern multiple choice tests were sophisticated enough to test the critical thinking skills and deep level of understanding that essay questions were intended to examine, he said.
And some bright pupils could miss out.
"Why should you penalise pupils who have a deep understanding of a subject but who, for one reason or another - perhaps because they are dyslexic - can't write well?"
His report says the government must resist any pressure to abandon external examinations altogether, as they are the only way to rigorously test performance and provide accountability to parents.
The head of the Qualifications and Curriculum Authority, Ken Boston, tendered his resignation after an inquiry into the failures in delivering Sats marks last year. He is currently suspended.
Children's Secretary Ed Balls scrapped the tests at age 14.
Mr Balls said GCSEs and A-levels provided sufficient accountability on the performance of secondary schools.
The government is looking at introducing an American-style "report card" to grade schools according to their performance in a number of areas.
A spokesperson for the Department for Children, Schools and Families, said: "Multiple choice questions play a valuable role in assessment, but there are no plans to make them the sole means of assessment in Sats, as it is still important to assess written skills and how pupils can develop an argument, for example."