Why do internet maps use Mercator?

I've often wondered why Google, as well as other internet map providers, use the Mercator projection. It was originally designed for nautical navigation by keeping lines of latitude perpendicular to lines of longitude. The cost was that land areas were distorted, and the distortion increases nearer the poles, making countries in very low or very high latitudes look bigger than they really are. Using the Mercator projection, Greenland looks bigger than Australia for example, but in fact Australia is about three times the area of Greenland.

The answer given by John H, a Google employee, is:

[Google] Maps uses Mercator because it preserves angles. The first launch of Maps actually did not use Mercator, and streets in high latitude places like Stockholm did not meet at right angles on the map the way they do in reality. While this distorts a ‘zoomed-out view’ of the map, it allows close-ups (street level) to appear more like reality. The majority of our users are looking down at the street level for businesses, directions, etc… so we're sticking with this projection for now. In the meantime, you might want to look at our favorite 3D view of the world.

For more information on this problem, its implications, and the reasons Google use Mercator, see Anders Kaseorg‘s answer to ‘Why does Google use the Mercator projection on their maps, as opposed to an equal-area proportion map?‘ His answer also references Joel H's answer (above) to its original question, ‘Why does Google maps use the inaccurate, ancient and distorted Mercator Projection?

So now I know why Mercator is used, I wanted to test projections to see how much difference it makes. I've chosen Reykjavik, Iceland, as it is the northernmost (i.e. highest latitude) capital city in the world, so it will accentuate any differences in projection. I also loved visiting Reykjavik, so it's nice to remind myself of my holiday there!

To explore this, I downloaded administrative boundary data of Iceland (country outline, regions) from DIVA-GIS and roads from geofabrik. I separated out the capital region then clipped the roads for just this region, leaving the following map (in EPSG:3857 Pseudo Mercator):

Reykjavik in EPSG:3857 (Pseudo Mercator) with roads

So let's take a look at some simple directions from the Hallgrimskirkja (for the awesome views) back in to town, making sure we take a couple of turns:

And the same directions in QGIS using the Psuedo Mercator projection:

Directions from Hallgrimskirkja to Lækjargata, Reykjavik, in Pseudo Mercator (internet maps) projection

And finally, the resultant directions when transformed to the WGS84 datum without projection:

Same directions without projection

The result is almost an isometric projection of the equivalent Google Map, and changes the angle of the left turn at the right-most point on the map from approximately 90° to 56°. Clearly the unprojected map is inferior for local directions compared to the map projected in Pseudo Mercator, and at high latitudes it makes a noticeable difference.