Once again, people misunderstand the Agnostic viewpoint. Nobody is claiming to believe in any of these things, but just accept them as vague possibilities. Given that a Unicorn under my bed magically appearing and disappearing pretty much violates our understanding of physics, we can reason that the chances of it being there are very small. You said yourself that science is a branch of knowledge that can never truly prove anything, so to deny something
completely on the basis of scientific reasoning is foolish.
I don't get what you mean by the term "impact", so please elaborate on that.
If you mean how does this affect our scientific understanding of the world, then there is no difference between the Agnostic and the Atheist. Again,
bacon said:
The agnostic doesn't believe in those things though. He just accepts that it's impossible to rationally speculate on the existence of something which cannot (currently) be empirically or analytically verified.
Science is based on analytical and empirical reasoning, so here there is no difference between the Agnostic and Atheist schools of thought. So that being said, if you say "Why would we?", then I can equally ask "Why favor Atheism over Agnosticism?".