LaTexLearner wrote:Does it have to be 1.5em? Could it also be 1.5ep or 1.53j?
No. Designers usually consider the basic height of a lower case character and the width of a (wide) lowercase character as a property for referencing. x was chosen as height sample, m as width sample. Other characters usually scale proportionally. That means, if n would be 80% of the width of an m, the relation stays the same if you would resize the font. The width of m is the reference.
LaTexLearner wrote:And would 1.5em change if the font changed the width of m? If so, wouldn't it be easier to set the default length, to, say, 0.6cm?
Yes, em changes with the m glyph. But, easier or not, there's a purpose: if your drawing should scale with the font, choose em and ex, if it should stay the same even if you would change to a larger font, choose cm, pt, or any other absolute value. The relative values em and ex are very useful, since you don't need to adjust a lot of absolute values in case of a font size change.
Stefan