Wizards need to harvest monsters for ingredients, spells, get fabled magic items and such. They're literally the ones that are most likely to go out into the boonies looking for stuff.
In the entire Player's Handbook, only the Guards and Wards spell mentions a monster part (Umber Hulk Blood) and since it doesn't have a cost associated with it, you can replace it with an arcane focus.
So, no, wizards don't need to harvest monsters at all, unless there is a plethora of such spells in Xanathars... eh, sure, I'll look. Aganazzer's Scorcher requires a red dragon scale (replaceable), Shadow of Moil requires an undead eyeball, but the wizard can make that themselves and order their undead to rip out their own eye instead of adventuring for it.
So, three spells total, only two of which would require adventuring. I'd say that pretty thoroughly debunks that.
And, magic items could be a thing. If they don't feel like making them themselves, but since they are rich and powerful, why not send a party of adventurers to do it for them?
Wizardry is not law. It's far more powerful and useful.
I'd say you are wrong on that part. You of all people should know that the law can be used viciously to destroy people.
Off the top of my head, four of the attorneys that I have worked with have been the sons of other attorneys all four of those worked with their fathers. One of those also had an uncle who was an attorney in the firm. Those are just the ones I know about. Families going into law happens a whole lot. Why? because it's lucrative and gives power. Much like wizardry, only wizardry gives more.
Yep, families go into law, but how many of them were taught by family?
You say wizardry can't be taught because they'd teach their kids if it could, but you are missing entire slews of reasons. Some people are just bad teachers, sometimes kids aren't interested in the family job, generally they send them to be taught by someone else.
And, you are just assuming that wizards don't teach their kids in the first place, which they could very well do, I mean, if you are born with magic, it is going to run in the family anyways.
Sure. Why go through the effort when you can pay others to do it. If there weren't schools, they'd have done it themselves.
Translate that to D&D and wizards will teach their kids unless there are wizard colleges to do it for them. Either way the D&D world would be flooded with wizards and it isn't.
You realize families are small right?
Why doesn't everyone know Gramma's secret recipe for pie, been passed down through the family for a hundred years.
Might be because while the family knows it, not everyone is in the family.