I think you are right. While I'm interested in sports governance/economics/history as a whole, I'm mainly dealing with figure skating, so biased towards the problems of this sport. Boxing rankings are fun, by the way. As far as I understand none of the four (!) sanctioning bodies in boxing have implemented anything resembling a mathematical model for rankings.
Re: extrinsic motivation. SDT (Self-Determination Theory) actually has quite a lot of studies on this matter. See Deci, Koestner and Ryan (1999) as an example [1] If you're designing reward/incentive system and want to maximize intrinsic motivation, what to choose – reward for showing up, reward for doing a task, reward for doing great or reward for winning?
Here is a quick breakdown of these contingencies:
1. Task-noncontingent – Reward is given simply for being present and does not specifically require actually being engaged with the target activity.
2. Engagement-contingent – Reward is given for spending time being engaged with the target activity.
3. Completion-contingent – Reward is given for completing a target activity (sometimes within a time limit).
4. Task-contingent – Refers to a larger category containing both engagement-contingent and completion-contingent rewards.
5. Performance-contingent – Reward is given for reaching a specific performance standard, for example, doing better than 80% of other people who have done it.
6. Competitively contingent – Reward is given to the winner of a competition and the loser gets lesser or no rewards.
Simplifying a bit, the results are – the further you go from 1 to 6, the stronger the detrimental effect on intrinsic motivation. In 6, for example, intrinsic motivation can be sustained only for the winners (because it carries a strong positive competence signal) but undermines it for everyone else.
Note that it's not always bad. In a private company, you may want to get rid of "underperformers", so rewarding excellence works fine.
[1] https://pubmed.ncbi.nlm.nih.gov/10589297/