Well, you can deny it all you wish, but if you want to go from California to Japan you maintain a straight course from point to point and you certainly aren't going around in a circle as the azimuthal equidistant projection would show. The ship I was on sailed directly from San Diego to Honolulu ; then sometimes a stop at Guam; and then on another straight course to Yokosuka, Japan. Always some compass heading.
I think you need to ask your questions to anyone in the navy or in the maritime service about sailing from one port to the other across any ocean.
Maybe this might be the reason for your question. You would sail one compass heading from San Diego to Honolulu. Then another one from Honolulu to Guam and another one from Guam to Japan. Do you understand this ?
We are NOT talking about San Diego-Honolulu-Japan which is not a straight line btw.
Besides, on a flat earth, going west (or east) means that you are sailing in a circle. Because of the large distances you are not aware of this on a ship or airplane.
We are discussing a route around the world. For example from Japan to Japan in a straight line from 'left to right' and from 'up to down'.
Did you sail/fly from Japan to Japan in a straight line?
My example was the usual type of operation in going from the USA to Japan. Ships usually didn't go direct to Japan. They usually made stops in between. But if you wanted to go non-stop.....Yes.....All you would need to do would be to plot your course and stay on that course. Yes, it would be a straight line at some compass bearing.
http://www.chriscruises.com/2015/07/the-viking-advantage-we-would-gladly-repeat-our-experience" Ocean cruise lines travel a straight line from port to port with passengers along for the ride, all the way."
I would suggest if you have any questions about ships or aircraft flying or sailing in "straight lines" you contact some cruise lines, shipping lines, or air lines. Ships and aircraft keep logs, you know. They are quite aware of the distances and courses they take in going from port to port, be it a seaport or an airport.
Another source for around the world cruises would be the Navies of any countries in the world. Many of the ships in the United States Navy make around the world cruises. Of course they keep a log of the distances and courses involved in these cruises.
Incidentally , the movie "A Night To Remember",( a movie about the Titanic disaster )contains some interesting material concerning how ships plot their courses. It is available on DVD.