“Would it perhaps be helpful if textbooks described the perfect as the present perfect as is normal in English?”
There is a difference–the Greek perfect can be used in a past context; the English present perfect can’t. [Update: On reconsidering this, I think it’s wrong. I can’t think of an instance where the Greek perfect indicative could be used in a past context. The pluperfect would be substituted for the perfect, but in my experience, the pluperfect is extremely rare, at least in the Geek I’ve read. However, Greek perfect participles can be used in a past-tense narration.] So maybe designating the Greek perfect as the present perfect would be more confusing.
I think it’s best to try to divorce our thinking about Greek verbal aspect (Aktionsart–this is the German term, which Godmy is familiar with, equivalent to “verbal aspect”) from English aspectual distinctions.
The Greek perfect is less used than the aorist, I think, because it is a highly specialized, “marked” verbal aspect/Aktionsart, and doesn’t normally come into play in straightforward narrations of events, one after the other. The two-way contrast between imperfect and aorist usually is adequate for this purpose. In narrative writing (e.g., history), the perfect isn’t often needed. But in speeches and dialogues, there’s probably more occasion to use it.
“He knocked and waited for the door to open.” Here “he knocked” would probably be rendered by an aorist participle because there’s no special reason to emphasize the continuing effect of the knocking. κρούσας ἔμενε. Using the perfect would add a special meaning to the verb. It’s difficult, but maybe not impossible, to imagine circumstances where this would be appropriate.
Here’s an example of knocking in the perfect, though it doesn’t refer to knocking on a door (Plato, Phaedrus 228e, which I found through LSJ; I haven’t looked into the context):
Φαῖδρος. παῦε. ἐκκέκρουκάς με ἐλπίδος, ὦ Σώκρατες, ἣν εἶχον ἐν σοὶ ὡς ἐγγυμνασόμενος. “Stop it. You’ve knocked out of me the hope I had of practicing on you, Socrates.”
As a result of Socrates’ previous “knocking,” i.e., something Socrates said, Phaedrus is currently in a state of having had his anticipation of practicing on Socrates knocked out of him. You wouldn’t use the perfect for the simple act of knocking on a door, but here the focus is on the effect of knocking.