Ehh sometimes you have additional results or insightful remarks that simply don't fit into the page limits. You may want to keep those for yourself and use them for a separate publications rather than give them away.
Also true, but the arxiv version is often (in my experience) containing the entire paper. Indeed, many conferences ask people to submit the full version to arXiv.
Aye, but in this context "full version" usually means "a version with more detailed proofs/results related to the paper's contributions", rather than "a version with additional contributions".
Why not? I love to peek at .tex file comments, and secretively hope that somebody somewhere is reading mine...