No Mercator projection is used because its the least weird conformal projection (you draw a straight line its really straight in the real world). If you are trying to plot a bearing at the scale of the planet you want to be using Mercator unless you are going over the pole :P That the same projection is then used for everything even when you don't need to preserve local angles isn't the fault of Mercator. That you think km lines on an atlas would be better than lat/long makes you crazy. A decimal day might be useful but a decimal year is not. A fractional decimal day is a completely useless reference of time for doing quantum mechanics, but perfectly reasonable for people planning their work. No one would get rid of the concept of "a day". A map that maybe only shows tens or hundreds of km might be fine but representing the whole world with an equal area map with all grid reference based on km isn't useful to many people who use maps a lot, especially as the world isn't describable in whole numbers of km! But does have absolute and continuous angles from the gravitational centre.
Lines on a Mercator map aren't straight on a globe.
They are constant-compass bearing, but that's not the same as straight.
Also, as defined by the French academy of science ~1800, the meter is 1/10,000,000th the distance from the north pole to the equator, on the meridian through Paris.
Not sure what your metre comment is about, but it turned out that definition wasn't accurate enough to confidently state the speed of light, so the speed of light was set to 299792458 m/s and a metre is consequently the distance light travels in a 299792458th of a second.
(The second is in turn precisely defined by particle physics.)
It's a reference to Justin_K's earlier statement "a Knot is standard for navigation world wide because the unit is standardized on earth's size".
If that justifies knot then it also justifies kilometers, because it too was originally standardized on the earth's size.
Neither are exactly the size as originally defined.
A modern knot is 1852 meters. One minute of latitude is "about 1,855.325 m on the WGS 84 ellipsoid" says https://en.wikipedia.org/wiki/Nautical_mile. The difference is 0.16%.
The shortest distance between two points on sphere is along the great circle that contains the points, and are the closest thing to a "straight line" you can have on a sphere.
Straight lines on a Mercator projection aren't great circles, they're rhumb lines, and if anything they're a spiral on the sphere, not straight.
If you are holding a globe that a useful definition. However, that's not what navigators are doing. We can look at the stars and a compass both of which make rhumb lines far more useful.
Rhumb lines may be useful for tiny vessels with only a compass and a map on board, but any commercial vessel, whether it is on the water or in the air, will follow the great circle route. It's the shortest and fastest way to go and it uses the least amount of fuel. Following rhumb lines just because they happen to be straight lines on Mercator projected maps would be silly.
It's not the 1800's any more. We have computers and stuff, we don't have to rely on techniques developed for a time when your navigational tools consisted of a map, a compass and a sextant.
Computers don't care about your maps and will plot a great circle route just fine. However, in the event of system failure you want a real backup. Which is why the navy still teaches people how to use a sextant. http://www.npr.org/2016/02/22/467210492/u-s-navy-brings-back...
Note: The actual deviation from a great circle route is generally fairly minimal in practice.
PS: GPS is just another system that really can fail.
The passage of time doesn't diminish the usefulness of local navigation techniques...
a Mercator projection will give you a bearing to steer to arrive at your destination, which can be followed by eye, autopilot, etc etc.
Calculating a great circle arc and plotting it, following a bearing which may only change by a degree or two but isn't constant, is an unnecessary complication on short routes.
Even commercial vessels will use those old techniques if they don't need to consider the longer range effects. Error correction in the human process is always a consideration.
(Not even talking about data entry errors in GPS systems, but that Malaysia - Melbourne story was Funny.)
