Yahoo only has a 15% stake in Ali Baba from what i can tell. So while Ali Baba is huge, it's not all Yahoo!
I have no special knowledge in this area, but my understanding is the Yahoo stake in Alibaba is purely an investment. That investment is worth a few tens of billions and Yahoo is retaining it to distribute it to shareholders as cash.
It's easy to value cash, so no need to negotiate with Verizon about it. It's a lot harder to place a value on the rest of Yahoo's business, and the value depends a lot on what the buyer will use the business for, so it makes sense for them to auction the business off to the highest bidder-Verizon.
I read somewhere that Mayer had a great rep at Google, but she was a product person, not an executive really.
Also in a limited sample of professional women I know, Mayer is uniformly hated, for talking the talk about helping women succeed while installing her own personal nanny outside her office. If every professional woman had a 24-hour nanny watching her kids right outside her office, breastfeeding and career advancement would be a lot easier for them too. Yahoo didn't make it that easy for women who weren't the CEO.