It is a legal document that has to be adhered to
I am surprised people still say this. Statements are obsolete where I work, and have been for years. Some of the eldest students might still be toting one around, but we have no requirement to act on them.
Some places still use them, but it is patchy, some people still try and insist they are legally binding, but in practice, this isn't enforceable.
As the OP says, the trouble with statements is they were granted to the parents of the pushiest, and often the richest parents, not to the children in most need.
A student arriving in my class with a statement, I would consider it a helpful indication of the type of problems they have, and the support appropriate. I would not consider it a reliable indication that they have more needs than a non statemented child, although I would expect it to be reasonably accurate.
We do annual reviews for most children with statements, and many children without, and use the term " statemented" very loosely, to mean the pupils with the most severe needs, rather than the ones that actually have statements.
It doesn't necessarily attract extra money, that is distributed quite differently now, according to the school