I assume this is just a bug (not a deliberate design choice). The context is always visible on the task line in the iPhone app and in the web app. It is very useful. I feel blind without it.

In addition (but this is a feature request), I would like to have the tags visible, too, on the task line, in all apps that are intended for larger screens (and maybe even on phones). I feel blind without it, and therefore do not use the tags feature as much as I would want to.