When it came time to...
Is the phrase technically correct, or is it an exercise of artistic license?
The phrase is perfectly valid. I have seen the phrase used mostly to convey some kind of a twist, as in:
When it came time to vote, the senator switched sides.
Seems perfectly fine to me, though would benefit from more context. E.g.:
When it came time to leave, she was ready.
Wouldn't "When it was time to..." be better?
I've found that "when the time came" is used more often than "when it came time". I personally have not found that either is incorrect so I suppose it just depends on the flow of your sentence and the context it is in.