As a contributor, particularly when I am editing, I often wish to maximize the screen real estate given to the editing tool.
I rarely will use left hand side links while editing, as I have swapped from a 'passive viewing' to 'interaction, task specific' mode of use.
A simple 'hide left hand nav' UI toggle would greatly improve the editing experience.
You can do this in either P2 or iD by pressing 'M' for maximise. If there were to be a visual equivalent it would probably be better implemented in the editor rather than the Rails port.
As @systemed says, both editors can already do this, and any issue of better exposing that functionality to the user is a matter to take up in the relevant editor's bug tracker.
Making the site more responsive is something that will almost certainly happen with the ongoing design work but it won't be relying on people manually showing and hiding things, rather it will simply respond to the available screen size.
Well there aren't really tickets for something as general as "design work" rather as people have specific suggestions (or preferably code) they open an issue or pull request for that.
See for example the form restructuring pull (#300) which was merged recently, or the map UI one (#328) which is currently in progress. Those are some of the first pieces of the changes.
Something as vague as "make the site more responsive" is not really a very helpful thing to have open though, as it not concrete enough to have a point when we would be able to objectively say that it is done.
So far as the concrete suggestion of providing a user triggerable way to make the map full size, that is not a direction I think we should pursue, so unless there is community consensus to the contrary I am inclined to leave that closed.
Improved responsiveness to differences in client screen size is definitely a goal though - we do already make the map more or less full size on phone size displays (or at least try to) but we should probably have a better story for intermediate size displays like tablets.