I don't think your plan is nearly as daft as others do. I was rather concerned when I thought you were proposing to leave your son alone for five entire days a week. But three hours a day, I think could be OK depending on the child. I certainly don't think it automatically constitutes neglect. Nor does the law: there is no legal minimum age for a child to be left alone.
Few experienced home educators would fault your idea on educational grounds. You are right that you can educate your son when you are not at work. And of course he will also be learning when he is playing alone and when he is with his grandparents. It looks quite different from the school model. But it often works. It is not such a rare approach.
It's all a question of whether he will be safe and happy unsupervised for three hours a day. Many hours spent alone can be lonely for a child, perhaps more lonely than for an adult as he doesn't have the same options of going out and socialising with other people. It isn't that he needs to BE with other people. It's that he needs access to other people when he wants to be with them, if you see what I mean. The fact that you presumably are only thinking of doing this for six months or so may mean it is not so hard on your son.
Personally I think the NSPCC guidelines are somewhat alarmist. I wouldn't have thought anyone on a home ed forum would be too inclined to pay them too much credence bearing in mind some of the misleading things they have said about home education! I have left a child this age alone for prolonged periods on a regular basis. I was, and am, confident that it was fine in that particular case.
If you do decide that your son needs less time left alone, there are other options you could explore. Childminder, maybe? Not necessarily for his every waking hour but just for one or two mornings a week to give him some company and a chance to get out of the house. Also, speaking of waking hours, you could reduce the number of his waking hours which he spends alone if you and he are happy for him to stay up later in the evening and wake up later in the morning. These days my teen sometimes doesn't even know if I've been out for a couple of hours in the morning! One of my friends (single working parent) often goes out leaving her tweens to sleep in for a few hours, and the childminder only arrives to collect them after they've got themselves up and had breakfast.
So yes, I think you need to give it some more thought but I wouldn't rule your plan out. You can also tinker with it as you go along. See how your son feels about it after a few weeks and whether you need to make adjustments.