One reason I heard is that guns wouldn't have been that effective on a balloon the size of a football field; mere pinpricks, basically. The balloon would leak,

One reason I heard is that guns wouldn't have been that effective on a balloon the size of a football field; mere pinpricks, basically. The balloon would leak, but not nearly fast enough to bring it down in a reasonable amount of time. Unless, of course, they unloaded thousands of rounds into it, which is probably more dangerous and less practical than taking it out of the sky with a missile.