Why is the Stereographic Projection not used for Navigation

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The mercators map is most often used to map a rhumb line (path of constant bearing) between two points due to its conformity, however, the stereographic projection is also conformal, so why do we use the mercators over the stereographic for navigation?

Additionally, explaining how to navigate with a stereographic projection with the following example would be helpful. For example, how would I plan my path from point A to point K? Would I draw a straight line between the two, and would that line be a rhumb line?

Edit: the cyan lines are the 85 and 80 degrees parallels, and S is the South Pole (this is a polar projection).

Thanks in advance! Apologies for the mess, mind only point A and point K