Play/Pause as an on/off toggle is still contextual within the music app. The play button is always going to be in the same place, and the pause button not much farther away. Music apps have also started displaying triangles over the album art.

Hamburger menu is an abstraction. Part of the blame here is on operating systems and their branded menu's (think Windows Start or OSX Apple menu). There's no standard to it, which is why native apps are a lot easier to navigate because they conform to what the user expects. That fragmentation grows when you divide by the user's browser, device, etc. It's just not standard and not contextual enough to be a standalone icon.

    why does × mean "close" when it's in the upper-right corner of a screen

But even ignoring the counterpoint to the idea that a UI element must be contextual within some category to be understandable, the idea that the hamburger menu isn't a standard OS abstraction is also just silly. Hamburger menus are for mobile devices, and in your points you're comparing them with navigation used on operating systems meant for desktops. On Android — the most-used mobile operating system in the world — the hamburger menu icon is part of the standard toolkit, is built directly into their SDK, and is called out explicitly in their specs for Material Design.