What my question is... Why can't children who have been expelled from hogwarts buy another wand from ollivander? I mean, when ron's wand snapped in the start of the second year, he went and got a new one. So why can't children that have been expelled get a new one too? Do they really expect them to go the rest of their lives as a squib? (seen as though that's what they would be without a wand).

I think that's the point yes. From Hagrid we learn that he isn't allowed to be doing magic after being expelled. You don't finish your training so are seen as, I guess, dangerous and unpredictable (as Hagrid's magic definately was) - not to mention that you're being punished. Pretty harsh I supose, and maybe Hagrid was an extreme case due to the severe nature of his alleged crime. But, I also think it would take a lot to be expelled in the first place, so then a ban is probably deserved. Trivial rule breaking would have been dealt with by detentions and point losses, so it would have to be something major. Maybe Hagrid is the only case in recent times. I don't think it would have happened often in any case.

So, perhaps not all expelled people were banned from magic altogether, but I would highly doubt there'd be more than a few expellees other than Hagrid if any. And if so their reasons for expulsion were probably bad enough to warrant such a punishment.

Yes I agree. You wouldn't have another wand if you had had the last one taken off you and destroyed. It's your punishment and they would make up a new rule If they thought it was too strict. But I understand what you're saying. That why do you have to suffer such a severe and disciplinary punishment and live the rest of your life as a muggle just because you've been expelled from school. (btw I'm not contradicting myself, I'm just saying both of my thoughts). Hope this helps.

I think that this rule is as such, because it takes an awful to get expelled from Hogwarts. I doubt something trivial like pranking (marauders, twins) and bullying (malfoy, harry) would have gotten you thrown out. I imagine you'd need to do something drastic, take Hagrid's expulsion for example. He was supposedly housing a monster that caused death - murder, almost.