I understand how annoying, painful, and disruptive to the user experience it is to have part of your app taken over by browser or OS default widgets and behavior is. It's sheer hell on UX. Yet the custom styling that would make it integrate smoothly would be a godsend for attackers and phishers.
The role that UX - and misuses of UX - play in security is often not considered deeply by highly sophisticated users.
Compared to that, one icon, that is the same as that of the company, is not that threatening.
Not only that, but if you consider a sign in form that wouldn't have a logo, it would be way easier to trick user into putting their credentials in, because the user wouldn't be able to differentiate them. Also OAuth is always branded AFAIK.
Users may also notice discrepancies in the logo, if it was cloned poorly. Though I can't think of a way someone couldn't forge a logo given all the possibilities. Adobe Illustrator can trace images into svg and there's plenty of companies' svg logos just in the google search.
I think the real answer is that allowing this kind of deep and arbitrary styling of interfaces is far more dangerous than it is helpful.