One problem with that is that, as I understand it (I'm not an academic), not citing a relevant paper makes you look ignorant and can lead to accusations of plagiarism or attempts to steal credit; more subtly, it can lead to the reviewer whose paper you didn't cite recommending that your paper not be published. So it's not about being competitive, exactly; it's more about being cooperative. If you don't cooperate, other researchers won't cooperate with you, and your career will founder.

For the most part, I don't think scientists care about the issue, except for being a bit annoyed with Elsevier. Most people don't care about most things that don't affect them directly. Scientists are people too. So rather than invest effort in activism, they mostly focus on their jobs and their families and stuff.