Any reason not to apply for funding as a grad student? The question is hypothetical, but it came up in a conversation and I'd like to see if we can come up with a logical analysis and conclusion. For various reasons, graduate students might not be inclined to apply for funding. 

By funding I mean grants or scholarships intended to support graduate students directly in the form of money given directly to the student. That is, I am not talking about applying for research scholarships intended to fund an experiment, buy equipment, etc. Here are a few (made up) examples.

Case 1 (Differential). I get 20000 of internal departmental funding but be encouraged by the department to apply for external funding. If I then get 5000 scholarship, then the departmental policy might be to drop the internal funding to 15000, so I don't apply for it.

Case 2 (Rich Student). I am very wealthy and I have no need for funding. I am a brilliant student and could probably get many different scholarships but I chose not to because I feel other students with less money need the money more.

The "Rich Student" scenario is slightly different than the "Differential" scenario. If I am rich then for sure some other poorer student could have gotten the money, whereas in the "Differential" scenario, I am now only getting 15000 so another student will get the 5000 anyway.

The problem with not applying for scholarships is that I don't get scholarships, and in many fields winning scholarships is good for your academic career. Perhaps in some fields this is more important than others.

Overwhelmingly I've heard that one should always apply for scholarships regardless of circumstances because of this. Of course theoretically, I could bypass my "rich student morality" by using it to do something useful for the community.

Personally, although I am not in these situations, I feel that it is most beneficial to always apply for scholarships, I would just like to have some kind of evidence that support this.

So to put this in a definitive question: for graduate students, is there ever a reason not to apply for at least a few available scholarships?
Reward to ratio of the application. If you already have some funding, and the additional funding is small compared to the time required to apply for it. For example, you have an NSF fellowship at ~$30k/yr, so it might not be worth applying to $2k scholarships which take a week or two of time.
Reward to ratio of the work. You don't want to take on a new project.
The project isn't relevant to your line of work.
You aren't qualified (GPA, citizenship, or status limitations)