For me, the point is just an easy low-tech way I can use at home to indicate I've gotten a knife up to some acceptable minimum standard of sharpness, without having to go test-cut on a bunch of tomatoes, boxes, or other tests that are expensive or a hassle. In practical terms: if I'm sharpening a kitchen knife, I'd rather find out
while I'm still at the stone, working on it, that it's not as sharp as I'd prefer yet. Rather than waiting until all my stones are cleaned and put away, and I'm slicing a tomato in the kitchen later, and find out it's still too dull. Or have to go cut a fresh tomato every time I sharpen the knife to find out it's sharp enough. That gets expensive.

Most of my knives I can test up to the more basic level I posted above and don't need the cigarette paper testing or extreme level of sharpness. It's just helpful to know which of these informal tests correlates to what level of real-world sharpness I can expect.
As for the extreme sharpness and edge testing, the cigarette paper and all that: for me at least, this is not a necessity, it's more a matter of interest, and a challenge, to see how far you can go in sharpening. I'd have no expectation that edges that sharp are going to survive very long. I won't even use the cigarette paper test probably 90% of my real world knives.