Of course it may have never crossed anyone's mind. Latin for Latin, greek for greek and never between shall meet.
You may be interested in my answer to the question Would Latin have ever been written in Greek letters or vice-versa?. As I discussed in that comment, Latin was sometimes written in Greek letters, for reasons that ranged from necessity (the writer or anticipated reader not knowing the Latin alphabet) to choice (showing off one's Greekness or knowledge of Greek, making a magic spell look cool), but it was never widespread or a political movement.