Hi OP, glad you've made it to the home ed board!
Taking your posts at face value, it sounds like you cope fine with life and your kids in general and it is literally ONLY public transport (especially at busy times) and the related rushing which you find overwhelming. If that is the case, there is no reason to suppose that you'd find home education particularly stressful. You say that you enjoy activities and doing educational things with your children. Sure, HE has its ups and downs, but it doesn't look like it would be harder or less pleasant for your family than for other families who are doing it.
I do think that most of the strong criticism you've been getting is actually an anti-HE prejudice. Imagine the opposite situation: a parent who has always home educated, who finds some aspect of HE overwhelming and is thinking of putting their children into school to get a break for herself, because she feels she simply cannot carry on home educating. In such a situation, everyone would urge her to put her needs first, because the kids would almost certainly be okay at school even if it isn't ideal for them. It's true that HE parents would likely suggest that she consider whether there is some other solution which would allow her to carry on HEing if that is what she wants to do, but nobody would accuse her of selfishness for putting her children into school if she cannot cope with home ed. You, on the other hand, are getting criticism for thinking of moving your kids from one reasonably good educational setting (school) to another reasonably good educational setting (home education) because you cannot cope with getting them to school. It's a double standard.
If one accepts that school and home ed are equally valid educational choices, then it is silly to demand that someone choose one over the other for the "right reasons". We do not criticise parents who choose school over home education because they want free childcare, or because they feel they cannot cope with spending so many hours with their kids, or because they feel unconfident of their own abilities. We do not criticise parents who choose a closer school rather than a more distant school because it makes for an easier school run. Unless your decision to home educate your children is likely to be disastrous for them, I don't see why your reasons should come under scrutiny.
I do agree that you will face challenges in home education. To an outsider (and possibly even to you) I don't think it's at all easy to predict whether home education will pan out well for your family. The transport challenge is an issue, no doubt about it, but will it ruin your children's happiness? That depends on so many things: how sociable your children are, what the population density is like in your area, whether you get on well with the other HE families who live nearby and go to the local home ed groups, whether you can manage the bus sometimes in order to go to the places your kids really want to go. So I would urge you to consider all this.
However, I don't see why you have to leave your kids at school while you figure that out. Why not take them out of school for a while, try home education and see how it goes? It is notoriously difficult to make sensible decisions while under immense stress. You will be in a better place to think it through when you aren't facing four buses a day at busy times. You will also be able to see how the social side of things works out for your children when they're not at school. This doesn't have to be a permanent decision. If home education doesn't suit, your children can go back to school. In fact, by the time they reach secondary age they can VERY easily go back to school, as they will be able to take themselves there. In that sense, it's worth remembering that this challenge is a temporary one. Whether or not you carry on with school now, in a few years your children will be in a position to make their own decision and you will be free of school-run stress.