I apologize for posting yet-another-gis-novice's confusion about CRSs, but I have researched the issue and am surprised by what I'm seeing.
In simplest form, I
- open a new project
- set On-the-fly (OTF) CRS transformation ON
- choosing NAD83/Conus Albers (a Projected, and not Geographic CRS) as the Project's CRS (same behavior choosing NAD83/UTM12N)
- load a 1x1-degree USGS ned30m raster layer which has an assoc. CRS of NAD83 (Geographic CRS)
- note that the layer comes in "skewed" (a North arrow "decoration" points NNE, about 1-o'clock)
- note that cursor coordinates appear to be in UTM meters
- note that the "ruler" distance-measuring tool appears to measure in meters, showing the raster to be approximately 88 x 112 kilometers
- set raster layer's Layer CRS to NAD83/Conus Albers (to match project's)
- note that the layer "disappears"
- note that coordinates of cursor still appear to be UTM meters
- choose Zoom to that layer
- note that map is now "squared up" with display (N arrow points N/up)
- BEFORE moving cursor over map, note that coordinates still appear to be in UTM meters (in "Coordinate:" box at bottom of display)
- AFTER moving cursor over map, note that the coordinates revert to geographic, Lat and Long
- after which the "ruler" tool measures the rectangle to be about 1 x 1 (must be degrees again)
As far as I can tell, I have done everything I can to alert QGIS 2.8.6 (similar behavior in 2.14 caused me to try the LTR) to the fact that I prefer meters.
I have also (following other advice I found here) tried Layer->SaveAs (to a Projected CRS), but the resulting 23+GB output hung-up QGIS, causing me to have to abort. (A separate problem owing to my naivete regarding choices I made--or rather, defaults I accepted--in the process of trying to save it.)
This is about as simple an example as I can imagine of wanting, say, to import an elevation file from the USGS and measure the distance around a prominent feature, like a mountain peak, in meters.
Again, I regret my need to broach the subject--again--but I would be deeply appreciative to either find out what I did wrong, or why the behavior I see makes Perfect Sense. Or both.
Update: The problem is still present in 2.18.23. Project->Properties->CoordDisp is set to MapUnits (automatic), but coords are still displaying in Lat/Long, even though the project CRS is Conus/Albers and the NED layer has been saved-out/reloaded--after relaunching QGIS 2.18--as a Conus/Albers CRS.
However IF I set the NED layer CRS to "NAD83" (its default), coordinates display in meters.