I can't see how they can abolish tutoring. The only way I could see would be for them to keep changing the style of tests, so that you didn't know exactly what to prepare for.
I don't agree fully agree with those who say that people weren't tutored in the old days. I went to a grammar school in the 1960s. I went to two junior schools because we moved house, and both schools were streamed rigidly. If you were in the A stream I think you got more push and more practice at the sort of exercises you would meet in the 11+. Your chances of passing from the B stream were extremely slender, as far as I recall. Some children were put in the B stream at age 7, so effectively got written off then.
Nor do I agree that on the whole the right people got into the grammar school - a lot of perfectly able children were deemed to be failures. The whole system was deeply unpopular because of this. You were tested on arithmetic and English and those funny shape matching sorts of questions. If you passed you were deemed capable, for example, of learning languages, but not if you went to the Secondary Modern. Now the sort of absurdity you got is the example of a close friend of mine 'failing' i.e. deemed to be unsuited to learning a foreign language but who already spoke Dutch because her mother was Dutch. (She later went to university and got a 2:1 and I could think of a good few more people like her too.)