Flash,
I presume, from your last post, that if you're flying a (regular) circuit in, say, a C150, and you're late downwind when you hear, say, a PA23 call "downwind", that you make no effort to locate the faster aircraft and ensure he's not going to fly into the back of you?
No - of course you will look out for him. Even though it's his responsibility to avoid you in this instance, you still like to know where he is.
Likewise, I'd be uncomfortable if someone called "initial" while I was downwind. Less so having read about various run-and-break incidents on PPRuNe, but I've still never actually seen one, so I really wouldn't know where to look with any kind of certainty.
FFF
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(FD - If an overtaking situation exists - and I'd say one aircraft doing a couple of hundred knots while the other is doing 70kts counts as overtaking - the aircraft being overtaken has right of way, and the responsibilty to avoid therefore belongs to the overtaking aircraft, as far as I'm aware.)