You must have only seen this phrase in places where it was used in the bright, sparkling, professorial manner assumed by your comment. I take no offense when it appears in a textbook, where the intent is to have me practice a skill. I do object to its appearance in a journal article, however; that is a context where you are supposed to communicate findings as clearly and concisely as possible. In particular, I've come across its use more and more often where one of the following likely applies:

1. it is doubtful that the author has actually done the work to prove his own assertion, and uses the phrase to cast his own burden on the reader,

2. the author has possibly done the work, but can't be bothered to condense it to the quality required for publication,

3. showing the work would clearly be useful for the target audience, but the author is more concerned with making the material appear difficult, or

4. the author is being ironic, because the assertion is either superfluous, outright incorrect, or known to be unprovable.

In fact, all these bad use-cases are common sources of humor among math nerds (http://www.jargon.net/jargonfile/e/exerciseleftasan.html), (http://abstrusegoose.com/12), (http://fasterdonuts.tumblr.com/post/4516834904/the-proof-is-...) ... so I think I'm being fair in calling this phrase a trope. As in, its overuse is well-known, tolerated, and occasionally ridiculed.

tldr: I am indeed complaining about bad writing, not the subject--specifically that "left as an exercise" has become a common idiom behind which bad writers in math and CS hide, and its inappropriate use is now all too common.