My kids are home educated. We are open to them going to school if ever they choose to (and we never badmouth or put school down in front of them), however so far they have shown no interest in going to school. They are thriving both academically and socially, mix with both school children and other home ed children and have a social life which is the envy of many of their school friends. They are involved in numerous activities both home ed and mainstream and are happy, bright, engaged children with a love of learning. Of all the people we know who are or were home educated, all of them are thriving and I haven't met a single one yet who regrets not having gone to school.
By contrast, I was miserable at school, was severely bullied by both pupils and teachers, could've done well academically but didn't because of how unhappy I was. I moved schools and although the second school was marginally better, by then the damage was already done. Like the OP, my experiences as a child still affect me now as an adult and if I could go back and change it I would never have gone to school.
Whilst i'm sorry that the OP feels they had a poor experience of home ed, I don't feel that their experience is a reflection of home ed as a whole, any more than my experience was reflective of all schools. Home education, just like school, is not a perfect model; done well children will thrive, done badly they won't.
Not all children will suit home ed and not all will suit school. However, it is my experience that most parents who choose to home educate are doing so precisely because they value their children's emotional wellbeing, and so the children are given a large say in their education and their opinions are valued highly. It is certainly not my experience that home education is something done on the whim of the parents with no thought to how it might impact the emotional wellbeing of the child. The vast majority of home educating parents are open to their child trying or going back to school should they ever want to, whereas how many schoolchildren are given the choice of whether they'd like to be home educated?
Can I garauntee that my children will look back on home education and feel it was the right thing for them? No. But they will grow up knowing that their opinions and choices were always valued, and that's something that not all children are lucky enough to have.
I don't think there needs to be stricter regulations around home education, the current regulations are more then sufficient. LAs are allowed to make informal enquiries about the educational provision children are receiving, and if they believe a suitable education is not being provided they have powers to issue a Notice To Satisfy, and if neccesary a School Attendance Order. Welfare concerns, as with any other child, are the remit of Social Services and it's worth noting that far from being invisible, home ed children are actually UNIQUELY visible, generally being seen by a much wider range of people than many school children. It's also worth noting that whilst schools are inspected by OFSTED, many schools with a good OFSTED rating are riddled with bullying and other problems, and many schools with a poor rating are nonetheless full of happy thriving children.
Could some home ed children 'slip through the net'? Perhaps, although it is worth noting that in the (very few) Serious Case Reviews where home education has been a feature, the children in question were already known to numerous agencies including Police and Social Services who failed in their duty of care. Numerous schoolchildren have also slipped through the net, Daniel Pelka being an obvious one, so school isn't a garauntee of anything. A one hour visit a few times a year from a Home Ed advisor is unlikely to pick up anything which the Police and Social Services can't.