Home educated children will still see doctors, dentists, optometrists, health visitors if they have younger siblings (or, like ours, the health visitors have an open policy for home educated children as a gateway to school nurses), and adults in many social situations. They may see more adults, mine certainly do. Children who are kept from these, however educated, are already red flagged by social services - not the local authority.
My children are known to the local authority, their details were passed on by a paediatrician when my oldest was 5. They showed up at the door the first time, we've seen them maybe 2-3 times since then in arranged visits (my eldest is 9/would be Y4). They told me that all they do is put the report I make and any portfolio the kids make in a folder to be kept if social services or others question their education. That's it. If they thought there was a safety issue, they would pass it on to social services - which anyone can already do anyways (and social services would pass education concerns to them). The LA doesn't do safeguarding for home educated children it knows. The two things are very much separate. Getting the LA to take over social services concern wouldn't work and isn't done anyways. I have no issue with out LA's involvement as ours is rather open and friendly and I generally just send loads of paperwork so our meetings are all brief, others often do as the vast majority home educators in the UK are those whose children were withdrawn from schools and have already had conflicts with the LA and the system in general (which makes it very different from the American system where it's more fueled by ideology, the two aren't very comparable). I find it quite understandable to not want to deal with a system that has already failed you if one can avoid it.
Personally, I'm like many parents here where I'm not sure of myself most of the time, I get stressed by things academic and social and in general, and worry about how I'm coping or if I'm doing the right thing. We're all in the middle of an awful illness and I've been calculating the catch-up time while my kids are all crashed out from it. But, my kids will be able to pick-up where they've left off when they're better without worrying about what they missed, the few changes made they can talk about with us rather than constant changes coming from someone who has never tried educating and making ideological changes rather than evidence-based education (I never understand people who talk about trust when the education system is so wrapped up in politician hands and the most recent education chaos in the system has been so damaging for so many) so they get a very consistent system [something I would have loved in school] as well as both an explanation for what's going on and input even at their age, they get time to actively learn emotional and social skills rather than being expected to pick them up just by being in a room with other people (to me, that's like expecting a musician by being in a room with a piano) and we can prioritise relationships. Being able to put their needs rather than the needs of an institution first and wanting to prevent the failures that I and so many I know experienced in the school systems would have to be the main appeal. Part of that being having the time and energy to expose them to far broader range of experiences at a time when history, literature, and so much more is being politically narrowed at the national level.
In terms of right curriculum, that differs a lot even with the research and evidence we have so far in education. I've read the national curriculum of several nations and there are a lot of differences in what is considered "right". Personally, I've found going to experts in those areas and getting their perspective and evidence quite revealing - and not that difficult to get. For example, my children's maths programme comes from the Centre for Innovation in Mathematics Teaching, they have free lesson plans and printable resources and workbooks on their website (though I prefer to buy their books, very good quality at £6 for a primary year, rather than mess with a printer, goes from reception to a-levels, even used in many schools). People passionate about their subject want to get this stuff out there, it's all there to be found and often with evidence to be freely reviewed and questioned.