phrase usage - Starting a sentence with "would that..."

In one of my favorite episodes of the TV show Community, "Conspiracy Theories and Interior Design", one of the characters says the following line:

Would that this desk were a time desk.

In the context of the episode, the meaning is clear: "I wish this desk were a time desk." The character is quoting a terribly written novel, and part of the humor is the combination of the attempted literary language ("Would that this desk were...") and the awful subject matter ("a time desk").

Here's my question:

Can you actually start a sentence with "Would that..." to mean "I wish that..."?

Is this phrase actually literary, or does it just sound literary and is actually incorrect?

Answer

To my surprise, I found brief explanations on Would that ...! in two of my grammar books.

In Collins COBUILD English Grammar, under entry 4.213 (regret: 'would that'),

In very old-fashion English, 'would' is used without a subject to express a wish that a situation might be different, or to express regret that something did not happen in the past. 'Would' is followed by a 'that'-clause.
'Are they better off now than they were two years ago?'--'Would that they were'
Would that the developments had been so easy.
[...]

In Longman English Grammar, under entry 11.42.4 'Would' and 'could' after 'wish' and 'if only',

[...]
Wishes expressed with would at the beginning of a sentence have either become obsolete (Would that it were true!) or have become fossilized idioms (Would to God I Knew! Would to God I had known!)

So, we can actually start a sentence with Would that ...!. But one grammar book refers to it as "old-fashion", and another refers to it as either "obsolete" or "have become fossilized idioms".