I fail to get how online services that support a “signature” make sense. I’m talking about those things that allow a user to draw something that almost looks like a real-world, hand-written signature on a screen on top of a line in a PDF. What am I missing?

Because Legally binding? rightsignature.com/legality/…

I am not disputing that signing a document electronically (i.e., with your private key) is a very good approach. Is this what this is referring to? Or does it refer to the drawing approach?

Your question had me look it up and was surprised to see that both the drawing approach and the digital(cryptography) one are on par and therefore admissible in court. I would have guessed the drawing approach as you suggested would be useless for that.