Why is the date left out of some academic papers?

There is often a substantial delay between when the author finishes a paper and when the paper is actually published. The author may not be totally aware of the publishing date. This is why the authors do not include the date.

The date is generally found in/on the book/proceedings that the paper is published in. This is the date that should be used for referencing a paper.

Re completion date: because updating it manually every time you modify a draft is time-consuming and error-prone, and TeX does not really offer an easy out-of-the-box automated solution (mainly because of its inherent limitations as a programming language).

If you use a preprint repository such as arXiv, you have a submission date there, and that is good enough for most purposes.

Some journals list submission, acceptance and publication date, but that is a decision of the publisher, not of the author.