It’s kind of stupid to use “Google Mercator” instead of a conformal cylindrical projection of an ellipsoid http://en.wikipedia.org/wiki/Mercator_projection#Generalizat...

However, the difference between that and Google Mercator is in practice pretty slight, since the flattening of the WGS84 ellipsoid is only about 1 part in 300. It’s not really that big a deal for most uses, IMO. Anyone with a use case where it matters can pick a different projection and either source data elsewhere or reproject the data from Google Maps or whatever similar source. If people are using Google Maps (or similar) data in inappropriate contexts, they should stop doing that.

The bigger problem is using a Mercator projection at all for small-scale (zoomed out) views of the map in contexts like a convenient online map viewer where less savvy viewers are likely to be mislead by the scale distortion, and get little benefit from having straight rhumb lines.

Couple of points. * It’s not trigonometry. The inverse of a proper ellipsoidal Mercator has no closed-form solution. * Data generally are in geographic coordinates, not map coordinates. If your data are in map coordinates, then definitely do not use Web Mercator unless your map coordinates are also Web Mercator. The same is true for any projection: You need to know what coordinates your source data are in (Geographic? Than what datum? Or map? Then what projection?). If there is a mismatch between your data coordinates and the projection you’re using, you have to convert between them. Web Mercator adds nothing new to that problem. * There is nothing “inconsistent” about Web Mercator formulas.

The simpler calculation was probably chosen because it would be a bad idea to store or analyze data in Web Mercator (so the projection is done each time a tile is rendered).

I wouldn't be terribly surprised if the person who set it all up chose the "wrong" radius (from your link) in order to make the projection even less useful for analysis.