I have read this post several times and I am honestly really struggling to understand why anyone who doesn't have money to burn would choose private education for the reasons that you have outlined here. That absolutely isn't a criticism - we all have different priorities and it's for you to spend your money in whatever way you choose. I just don't get it.
I mean, the sports facilities do sound amazing, and far beyond what any state primary school could offer. My dd only had the chance to try stuff like abseiling, archery, climbing and sailing on school residentials, and not as part of her regular PE. They didn't have their own pool or tennis courts either, though they did have use of the outstanding facilities at the local university as well as the local leisure centre. However, if my dd had fallen in love with one of the activities through trying it on a residential, I could have easily facilitated her doing this outside of school for a fraction of the cost of private school fees, with the added benefit that it would give her access to a different group of friends in addition to the ones she made at school.
Same with music, though the provision at my dd's state primary happened to be outstanding in this area in any case. But my own state school was pretty average with regard to music so my parents facilitated ultra-musical dd to do it outside of school instead. She is now doing the same with her son.
Re design and technology, this is part of the national curriculum for state primary school children so I'm surprised that your local school doesn't offer it. Academies and free schools don't actually have to follow the NC if they decide not to, but I think it would be pretty hard for them to meet the ofsted requirement of offering a broad and balanced curriculum if they cut out whole subject areas, so not sure how that works. DD's school certainly didn't have any fancy facilities to write home about, but this didn't stop them doing some pretty cool projects at primary school - I remember them making little lamps, designing and making photo frames, building solar powered cars etc. Again, they often had input from the local uni, and kids who showed a particular talent in that area were invited to go and do workshops at the uni etc. Her school did have a kitchen and they did cooking from reception onwards, though not terribly often. I think this was more about space in the timetable than lack of facilities though. Can't remember if cooking is a NC requirement or not off the top of my head, so maybe some schools don't offer it. I would be surprised if many don't though.
I actually see the 80 children per year group as a good thing, not a negative, so I am struggling to understand your perspective on that. Presumably you understand that 80 in a year group doesn't mean 80 in a class?! Infant class sizes are generally not permitted to go over 30 children per class in any case (there are some exceptions). They can exceed 30 in KS2 but in our experience, they rarely went much beyond that. DD's primary class typically hovered at around 28-31, with lots of smaller group teaching mixed in. E.g. dd used to get taken out as part of a group of 5 or 6 kids who were particularly good at maths. This is where the bigger year-group cohort was advantageous in my view, as there is more potential to find kids who are working at similar levels to your dc and/or kids who share similar interests etc. I would feel that a year group of 30 would be rather limited. I do understand why some people would prioritise small class sizes if that year group is split into two classes of 15, for example, but that doesn't seem to be the case from what you have said. And there are very few economies of scale for a school with only 150 children, so the fees that you are paying wouldn't necessarily stretch very far after they have paid for all of the lovely facilities that you have mentioned. That would definitely be a concern for me - if they are charging typical private school fees, then either they're cutting corners elsewhere, or their business model is not very sustainable imo.
As for bullying...it can happen in any school. Private schools may or may not be good at dealing with it. Same goes for state. It isn't about the sector.
I am not knocking your choice. If you feel that it's worth paying for all the shiny facilities because you think it will give your dc a better quality of life or whatever, then that's a totally valid choice. I just don't understand it at all, personally. Having ended up with an only child not through choice (secondary infertility), we could have comfortably afforded private school fees for dd, but we looked at the various options and concluded it wasn't worth it. The local private schools did have beautiful buildings and great facilties, but this just seemed like superficial gloss to me. When you actually drilled down and looked at the quality of the education on offer, there wasn't really any difference, and I felt that it would be easy to fill any gaps with regard to extracurricular activities etc by doing stuff outside of school. Fair enough if your evaluation of the options is different - you will be looking at different individual schools in any case - but I struggle to get my head around why you think it would be worth investing tens of thousands of pounds for the things that you have mentioned.
But anyway, regardless of all that, it doesn't really sound like you want a second baby. I think it's fine to stop at one if that's what you want, and there are many advantages to it. We didn't plan to have only one child, and I worried about dd not having a sibling for a long time, but actually I didn't need to. She has thrived as an only child. She has brilliant social skills, lots of friends and is never lonely. She has never wanted a sibling and has always said that she can't miss what she never had. She also notes that, while some of her friends have lovely relationships with their siblings, many don't get on and me have siblings who make their lives distinctly more difficult.
And as she has seen me dealing singlehandedly with my elderly parents despite having a sibling, she knows that having siblings wouldn't necessarily make a difference at that stage of life either! So don't feel that your child will miss out if you decide not to have another.... there are no guarantees about how they will feel either way. So you need to do what's right for you, and frankly, you don't sound sold on the idea of another baby!
And while I don't really see the benefits of private education particularly myself, I think there is an element of truth in the fact that having one child enables you to give that child advantages and opportunities that you might not be able to afford if you had more than one. For us, that was as much about time and logistics as it was about financial resource. For example, dd has a hobby that has involved travelling to different parts of the country at weekends, overnight stays etc. It has been incredibly easy for me to facilitate this because I haven't had other kids to think about, whereas for families with siblings, it is more complicated. They either have to split the family up for the weekend, with one parent going to the activity and the other staying at home/going to a different activity with a different child, or the other kids have to trail along with the one doing the activity, sitting on screens to pass the time etc. And on quite a few occasions, kids have been told that they can't go because it won't fit around the wider family etc. This is something that dd has really appreciated as an only child because we have had the freedom to take every opportunity that has come her way - and it hasn't made her spoilt in the slightest, she recognises how lucky she has been in this regard. One of the many unexpected benefits of having an only child that I hadn't really thought of previously.