I understand your motivations, and agree that it looks cleaner and would be more difficult to steal. But, I don't know if it would be lighter than say a thin-wire Wald style basket, or even a wicker basket, although their mounts may make them more prone to theft and not clean looking.

My two cents: A deeper basket may be more secure for a purse and sweatshirt while riding as there is less change of the purse bouncing out. And depending on where she (and you) ride, a front bag big enough to hold the purse that has a zipper or strap may be even better so that a passerby can't see and grab the purse or sweatshirt, and also the purse would be protected in the event of a surprise rain shower. At the very least, if you go with a shallow basket, make sure the purse is bungied (through the straps) or cargo netted.

Whatever you choose to do, she's lucky to have a thoughtful and supportive guy like you.