The chamfer makes a socket a lot stronger. It has to do with something engineers call "notching effects".
It involves a lot of things, but to keep it simple - if you have a sharp notch, it weakens the material a lot. A smooth transition relieves stress a lot.
If you have a simple shaft with some transitions, the "radius" relief (marked "r") makes it considerably stronger than a sharp transition. The "u" groove further helps relieve the stress in the axle:
If you need a flat surface for e.g. a bearing, there are many techniques:
So to go back to your question. The chamfer helps spread the load a great deal.
Instead of the red area being concentrated, it goes further. Peak stress is smaller because it gets distributed over all of the material.
The smaller the chamfer the smaller the peak stress. A 12 point socket actually distributes stress nicer than a 6 point one (but at this point it is hard to say which is stronger, cause the extra material in a 6 point does play a certain role too, so it can go either way) because it is more circular.
If you use a very small chamfer on the end of a socket, I expect it wants to crack along one of the edges of the 6 point broaching inside of the socket. The end of the socket is where it wants to "spread" when it fails, and that's surely always the weakest point of it...
So just by using my logic, if you have a larger chamfer you can afford to make a thinner walled socket. If you have a small chamfer you need to compensate with a slightly thicker wall to withstand the same force. It's up to the socket manufacturers to find the most useful balance of those two factors and how safe they want to make their sockets...
That's how I see it. I think in theory that's how it is. In practice, maybe a smaller chamfer does not affect it a great deal. But IMO considering sockets are made for a century I'm sure the manufacturers made countless real tests to determine the optimal chamfers or radiuses on its shape.