The situation is very different to when we were the age to do 11+. People often say that back in the past they weren't prepared and passed, so tutoring or home preparation isn't needed, but it is all a lot more competitive now and the situation of 30 years ago isn't terribly relevant.
And regarding relying on primary schools - well they will have covered the NC to the end of Yr 5 stuff, but Yr 6 stuff can come up too, plus many test VR and NVR too which aren't covered and exam skills are not covered - and when people say schools should spend time on this stuff, they forget that s hooks are already hard pressed to cover the curriculum they have to cover and not everyone will sit the 11+ - tiny numbers in many areas, so it would be a waste of resources to devote time to it.
In the end, it's very competitive to get in. In super selective areas where there might be 10 or more applicants per place, being on top table for maths and English won't be enough for all the children in that situation to get in. Lots will score very highly and many will be very clever and the difference between a place and not getting a place might come down to having been drilled in timing or accuracy. Even in full grammar areas, lots of people want a grammar place and see preparation as the best way to give the best chance in what is a one-time opportunity.
I don't think paid for tutoring is necessary, but some form of familiarisation is - it can be done by parents using some books or a website (most parents have the ability to track down resources and deliver this - but some won't be able to do it) or a paid for tutor. It doesn't have to be months and months or years. The key is to be familiar with the different styles of questions that come up and to have practised timing - if your child has done those 2 things with a tutor or with a parent, they are familiarised and if they are clever, are in a position to show off their best. If they are clever, but have never seen the kind of questions that come up or have never done timed work, then they may well fall down by not finishing due to having to spend too long just getting to grips with what the questions mean and not having a clear enough sense of how fast they need to work to finish. They might be cleverer than someone else who has been familiarised and who pips them at the post just because they were able to finish or recognised the questions.
Few people would send their child into an exam with no idea of the kind of things that might come up or having done no practice of timing. Why would anyone do this with an exam which genuinely is a one time only opportunity, unless they are not bothered at all about the result?
Some people can't seem to see a middle ground between no preparation and cramming for years. There is a middle ground. It probably is true that if excessive cramming for years is necessary to squeak in, then it might be a struggle to keep up once at the school, but having had some preparation really isn't an indicator that a child isn't up to it - it really isn't. And when people say they didn't do any familiarisation at all because they were worried that their child then wouldn't cope if they got in, I have to say, I don't really believe that argument. I think the reality is that people say that when they simply haven't got their act together to either get some books or a website or a tutor. Anyone who has given 11+ some proper consideration and done some research into it quickly realises it is very competitive and even if cramming for months or having a tutor isn't necessary, some familiarisation is, and at doing nothing at all just isn't giving any child a best chance of a place.