I guess the part of it being a public proposal helps here. Each coworker has a mental profile of the one making the proposal, and can judge to some extent if they are the kind of person to live above their means or to work above their means. In a sense that's a knowledge value created during the day-to-day work that you just throw away if you don't apply to this HR management problem.
A lot of your examples are somewhat linked to the issue of having just one person with a very limited supply of knowledge about their staff decide on salaries.
I want a $1M /yr salary because I want to give $900k to Doctors Without Borders. Surely that is a better idea than the CTO's Tesla Roadster and Palm Springs winter house, right?
Sure, I get that it's public, and that the coworkers should know the raise-asker well enough to understand where they're are coming from, but I still don't get how the "personal needs" thing should factor in at all. The living-within-one's-means thing was just an example. There are tons of reasons why you might want more money, but very few where you actually need it, assuming you've made reasonably good financial choices up to that point. And yeah, even with the best intentions regarding money, sometimes people still get kicked in the ass, but I still question if "having some bad luck with money" is a reasonable justification for giving someone a raise. I'm fairly convinced it isn't.
I'm not sure the one-person-decides bit really applies here. I object to "personal needs" being used as evidence for or against giving someone a raise, regardless of whether it's one person making the decision or many, or whether it's made by someone who knows the person and their work deeply, or only has superficial knowledge. I just don't think that matters for this particular case.
A lot of your examples are somewhat linked to the issue of having just one person with a very limited supply of knowledge about their staff decide on salaries.