"Plus do you pay for the HE groups and activities that have been mentioned?"
Yes we have to pay for some things-but we have become very resourceful as a community, to use free amenities, or negotiate educational rates, so we get things very cheaply indeed!
I'm always gobsmacked when people tell me the cost of bowling or ice skating for instance, outside of school days. We often get these things at about a quarter of the normal price-and of course when we use them, there are no crowds!

and then we don't have to pay for school uniforms, or trendy clothes (the need for 'labels' seems to disappear, when teens leave school to HE) or any of the multiple costs associated with school-of which there seems to be lots of threads on mumsnet. But I guess it's swings and roundabouts there.
"seems to me that it's really only a choice for well-off families"
I know literally hundreds of HE families now, from all over the country. I know two HE families that I would consider to be well off. The overwhelming majority in my experience, HE on a very limited budget. A large number of us, are on a very low income indeed.
Most of us don't use tutors either-simply can't afford them, even if we wanted to use them. We employed a music tutor in the last two years, as DD2 felt she needed to catch up with music theory quickly. To do that, we've had to give up something else.
There are HE camps throughout the summer, all of which are none profit making, and for many of us that is our only holidays.
The biggest costs for us, was transport to get to places. I also gave up on a career to do this, and now work part time at a much lower paid job.
I drive an old car now, we rarely bought any new resources, instead making use of FreeCycle, Ebay, Amazon second hand, charity shops and car boots sales.
The financial hardships (which I guess many would consider a downside, but we've just got used to it and live quite frugally) are more than made up for though, by the startlingly good results. We have often asked the children, if they have any regrets, if they would like the lifestyle their cousins have for instance, with foreign holidays, newer car, financial support through Uni. They could have chosen differently too, I could have picked my career back up, earned very well and lived the materially richer lifestyle.
They have consistently chosen this autonomous HE life on a very limited budget, over that. From quite an early stage in our HER journey, it became their lifestyle choice too. Interestingly, given half a chance their cousins would have made the same choices..... But it wasn't my sister's choice of what is right for her family though, and I respect that.
I really haven't had any other 'cons' to HE. It's 'pros' all the way for us.
We've had a wonderful life with these three, far far better than the one we had before they came out of school, or the one we had with their brother when he went all the way through school.
We have no regrets at all.
None.