Earlier quoted context omitted.
I'm an accessibility engineer and hamburger menus on mobile are almost always completely inaccessible. A majority of the time they need to be fixed in order to accommodate visually impaired users or users who depend on VoiceOver or other screen reading technologies. Its practically a default issue at this point.
What is the preferred design?
Enlarging the menu so its easier to find with screen reader tools like TalkBack and VoiceOver has been somewhat effective. However, if you have split menu's, login, search and other features, you start running into complex design issues with where to put all of those and whether you want to stuff them all in the mobile menu, outside the menu or a combination of the two. When you start putting features like search and login into the mobile menu, that also creates more accessibility issues as well.
Designing for accessibility can get really complex, really fast and I'm not sure there's really a solid design pattern yet that addresses all of the issues we're seeing now.
I know that's not a great answer, but it just highlights the complexity of designing for accessibility.