I tested this on an Android phone and tablet, but from Googling this seems to affect all touch-based devices. I mention

You can't drag and drop on mobile devices as the click and hold of the "mouse" is grabbed by the touch browser to enable scrolling, swiping, pinching etc

To be precise you can actually move things, but it's more like a very tricky video game than a simple user interaction. The key seems to be hold for long enough to trigger the drag, but not too long, no more than 1/4 of a second. If you repeatedly swipe like that then you can eventually move things, but only if you like a challenge.

I'm currently investigating disabling this stuff via CSS media queries on devices smaller than 1024px (i.e. iPad in landscape orientation). This will just force the visibility of the basic HTML version, and hide the JS version.

But it would seem likely that the mobile browsers advertise this lack of support in some way via javascript, and Moodle could check that before enabling this stuff.

Specific instances:

1. the "you can drag and drop files" message appears at the top of courses, but doesn't apply to mobile devices
2. drag and drop reorganise course sections
3. drag and drop reorganise course activities

I assume block moving is the same but forgot to check.

Another angle on this is performance, as it's fairly noticeable the time that Moodle spends doing javascripty things on the course page in edit mode. This is even worse when I know that I'm going to override what it's doing.