I appreciate that your examples support your suggestion that all repetitions could be punished to white.
My goal here is not so much to defend this suggestion but to show that the current statement of the repetition rule is dubious. In the first situation, it looks not fair to punish white (and neither black). Of course, stating that white always loses on repetitions is a way to solve all the issues I showcase here.
It would not be fair to leave white defenseless
Well it depends how you formulate the win conditions. If you state that the goal for black is to prevent white from putting the king in safety, repeting the moves is a way to do it. After all, white is besieged, and a besieged opponent loses if he doesn't win quickly enough. This was my suggestion about a "starving rule". Actually one could even extend it and include repetitions in "if no capture is made in 100 moves white loses". This indeed implies that white loses on repetitions.
I think I was too quick with this one.
Isn't this a clue that the rule is unclear? Even an experimented player like you struggles to interpret it correctly
So the king attempts to break out, causes repeating and loses.
So back to this formulation in terms of who is blocking. I see 3 issues with this one.
1/ This formulation is not equivalent to the current formulation of the rule. See the position below:
Who "causes" the repetition? Well, white is not threatening anything, he just tries to not die. On the other hand, black has clearly the choice. So my intuition tells me that black causes the repetition. But it is black who is blocking white.
2/ This formulation is not fair to white.
As already mentioned, the goal of the game for white is to find open paths and the goal for black is to block white. So this formulation leaves white defenseless in many cases. Like in the previous position. It looks paradoxical to reject by virtue of fairness the simplest rule saying that white always loses, while the alternative statement is unfair to white.
3/ Up to now, I actually have no problem with the formulation in terms of who is blocking. I don't care if it is fair or not, the game is already asymmetrical to start with... The only issue is that it is actually not the statement currently written in the Copenhagen rules, but ok. However, it has a major issue when the repetition involves more than 2 stones (repetition cycle, or board position repetition). In this case, both players could block something alternatively. Look at the following position:
White has almost achieved an edge fort, while black is in a quite good position. The repetition is done in 4 steps shown below:
Now imagine you're a referee at a tournament. Black stops the timer, calls you, and says:
"Mister referee, white is violating the repetition rule! He wants to get his king in the edge fort, so I block with move 1. Then he plays move 2 and threatens to capture my pawn. Since I don't really care about the capture, I play move 3 to seal the corner. Then white plays move 4, threatening to enter again inside the edge fort. So I block with move 5. Then white threatens to capture again with move 6, but again, I don't care, so I play the innocent move 7, and white threatens to enter again! I'm the one blocking the king with move 1 and move 5! It's the king who seeks the open path!"
But white replies:
"Mister referee, with all respects, I don't agree with my dear opponent. It is me who keeps blocking black. Indeed move 1 threatens to capture my pawn in c10, so I block with move 2. Then move 3 threatens to capture my pawn in c11, so I block with move 4. Then move 5 threatens to capture my c11 pawn again, so I block with move 6. And finally move 7 threatens to capture my pawn in c10, and I block with the king."
Now you, referee, must take a decision: who should break the repetition cycle?