I think the rule should balance the efforts and capabilities of the winner by material with the smart loser who found the threefold repetition in the first place.
Example : Instead of 1/2 - 1/2 , there should be a system where games are given rating points out of 10 lets say and the person winning by material gets 9 of the 10 points and the person who found perpetual gets 5 out of the 10 points . This gives the loser a draw and the winner a winning accomplishment based on effort .
In my opinion, if we're including half-wins, the one checking in perpetual check gets the half-win.
They are the one chasing the king so they are clearly the one in the dominant postion.
Two things :
(a) 5 out of 10 points is a half win which is what the repeater is receiving
(b) The one repeating is not in a dominant position as those in a dominant position have no need to repeat and claim draws rather those whose positions are falling apart like watered bread or those who have to in order to not lose they repeat thus making their positions weaker than the person being repeatedly checked. Also why repeater should get 5 out of 10 and non-repeater 9 out of 10 .
Conventionally, a "half win" means you get more points than a draw but less than a win, and your opponent gets less points than a draw but more than a loss. This is not what you are describing.
On your other point:
1) The checking player can be regarded in a dominant postion because they are the closest to checkmate. Perpetual check generally invovles multiple instances where there is only one legal move: if that square were to be removed somehow on any of these moves it would be checkmate.
2) Using the analogy of a war, if a king is eternally running for their life away from an opposing army and the other is not; they are losing, regardless of how big their army is.
3) It is true that the checker in perpetual check is generally losing otherwise. However this is a circular argiment, as it is only true *because* a perpetual check ends in a draw. If it ended in a half-win for the checker (even if it were only 5.1 points going by your system), some people in otherwise somewhat winning positions would be incentivised to go for a perpetual check; and because of that winning postion they would find it easier to do so.
In a few months. My peak was 1818 now it's under 1500!