That's rarely how they are used though, much more often they're used to replace the horizontal top menu bar.

They are for rarely-used actions. The corollary is that frequently-used actions are surfaced directly in the header bar instead of buried in menus. This is almost universally good. I say "almost" because content creation applications have so many actions that a menu bar sometimes makes sense; I'm thinking in particular of Inkscape with three sides of the window occupied by icons and a bizarre hamburger icon in the bottom of the right panel for some reason.

I don't disagree, but I think that's another reason they exist beyond screen real estate on mobile. Context menus take no screen space, but they don't play nice with touch.

There are plenty of alternative paradigms on touch interfaces, both two finger tap (on capable devices) as well as side-swipe are used to bring up menus that are as contextful (or more) than the burger menu.

"Long-tap" (tap and hold for a second) is another right-click alternative I've seen used to great effect on touch interfaces.

It works sometimes but it seems like drag me and it's really awkward when something can/should be both dragged or right clicked.

Touch and hold is fine as a right click.

But it barely exists anymore. It was common in early Android, not anymore. I think the reason was bad discoverability... which is true. But not having the functionality is worse.

Agreed!