Thank you for all the answers, but it looks like I was misunderstood a bit. Thanks @Koepel for emphasizing this. Probably my rusty English, sorry
Let me try to explain this in other words.
My goal is not to execute any other command / code segment while I'm waiting. I want to wait as wait it is, do nothing at all. Just waiting. However, I realized if I use delay after writing to a servo:
delay(500); //meant to wait for the servo to reach 0 pos, but see below, it doesn't work
then, if the servo was far from the target position, zero in this case, e.g. it was at angle 40 or more, the delay command interrupts the servo, so it stops moving toward the zero position and stays at whatever angle it was at the moment the code reached the delay(). E.g. it stops moving around angle 25 or so (in case of an initial 40).
I was puzzled and looked up what's going on and found this in the docs about delay():
"(...)No other reading of sensors, mathematical calculations, or pin manipulation can go on during the delay function, so in effect, it brings most other activity to a halt."
So what it says in my read is, if one uses delay(), Arduino (basically) stops working. Like if I "paused the whole thing". So my assumption is, this is the error, as Arduino stopped telling the servo to keep moving to reach zero angle, as delay() "froze" it (by interrupting "pin manipulation", which Servo.h probably does).
My plan is, to implement a "soft delay". A method, which interrupts my code but only my code, while Arduino in the mean time keeps doing its thing, whatever it was (e.g. keep driving the servo).
I read millis() is just a number, so it's kinda harmless reading it. My thinking was, if I keep looping on nothing for 'n' seconds, my code is interrupted (which is fine!), but nothing else, so the servo should reach the target position, whatever it is, i.e. no matter how far it was when it started moving as Arduino keeps commanding it (which it seems it doesn't do when delay() is called).
But something in the back of my head tells me there's a huge misinterpretation from me according to this, hence I fired away the question if this is the right way to re-implement delay in a harmless way.
(I'm not around my device right now so can't try atm)