Although the number of councils with serious failings has fallen dramatically in recent years, very few achieve the highest grades, said David Singleton, head of the LEA division at the Office for Standards in Education.
In keeping with the education watchdog's new "softer" image, its future role should be more about highlighting and sharing the positive rather than the negative, he said.
"The failing LEA is becoming a rare bird and that is a real cause for satisfaction," Mr Singleton told the National Association of Educational Inspectors, Advisers and Consultants.
"Of the last 50 authorities inspected, only one was graded seven, the lowest grade, and five received grade six.
"But the other side of the coin is that real excellence is still rare, with only one LEA achieving grade one - the highest - and six achieving grade two.
"So the inspection system needs to be much more attuned now to promoting excellence than to rooting out failure.
"We need to have a fanatical regime with a view to finding good practice and disseminating it."
LEAs could also expect their OFSTED visits to be much shorter, he said.
At present, inspectors spend around 60 days with each authority but this period would fall to 20 days in cases where few problems were uncovered.
Mr Singleton also called on the Government to reform the present system of funding schools through LEAs, branding it "bizarre" and "perverse".
He said: "At the moment you have an LEA that is there to assist school improvement but the way they get their own money is by taking it from schools budgets.
"If we are serious about LEA support for autonomous schools, we need to fund them separately."
Mr Singleton admitted that the link between inspection and improving standards was hard to prove, but added: "Although I see inspection as crucial to driving up standards, the fundamental purpose of inspection is to provide information to consumers and decision-makers.
"I think there is an awful danger in giving an inspector a stake in improvement because it opens up the temptation to find improvement where there has not been any."