The cup & saucer may have had a class purpose to it. IOW originally only the aristocracy (rich) would have such things, and the saucer allowed the beverage to be served without the filthy, uncouth, lower-class servant’s hands touching the actual beverage container at all. 
There may be exceptions but for the most part I’ve found that mug designers go for a rustic or homey look which means thick ceramic. This tends to promote dribbling of coffee down the side and I consider it unsightly when I see it on my own mug. (I don’t care one way or the other with regard to other peoples’.). Another issue I have with mugs is that they’re usually dark, and I believe strongly that coffee should be drunk from white cups or mugs, or at most of some very light color. The mugs I do use are all white apart from any mottoes or other designs, but otherwise I gravitate towards cups and saucers. I don’t usually use delicate ones of china, though.
I always found the empty packet from the sweetener to be useful for the dampened stirring spoon.
Definitely agree that mugs are for when the coffee/tea is prepared to the specific tastes of the person, whereas cup/saucer allows for people to adjust their own (space for spoon and nibbles).
I’d also have thought that the saucer acts as a coaster to protect delicate furniture from the heat of the beverage.
Tea cups, having a lower centre of gravity, are much more stable than coffee mugs.
Saucers, having a relatively narrow depression for setting the mug in, reduce stability. If the mug is neatly seated in the depression it would, at best, be no less stable than sitting on a flat table.
Say what? They have that relatively narrow base. Mugs are much more stable.
Say what? Tea cups have small bases and wider mouths. Mugs are the same dimension from top to bottom (except for the ones above with a wider base).
A mug won’t fit in the depression, and might sit on a saucer but might not fit well. You are correct, it wouldn’t be any more stable on a saucer.
I think the saucers are probably a Victorian thing. Everything was prim and proper for them. They’re the folks that dreamed up separate utensils for every kind of dish, so a soup spoon and a pudding spoon and a tea spoon and a broth spoon are all different items with unique shapes.
A teacup by itself may be less stable, but a cup and saucer together will be more stable in many situations where a table is not conveniently available. For instance, I sleep on the left side of the bed, so when we have our coffee, I use a cup and saucer as this allows me to put my coffee to my right, on the bed itself. Similarly, I can put my tea down on the sofa next to me.
For less formal cup and saucer sets, where the cups may be wider, the central depression will indeed accommodate many mugs; once in awhile I’ll use the mug-and-saucer combo this way.