I can see how it might appear reckless, but it's just not. How can it be? God is Love, and God does what He does on purpose, with purpose, with care, with design, with intention. All of these things are the direct opposite of recklessness. Do we see Him or His Love (which are one and the same) ever described in Scripture as "reckless." I don't know. I don't think so...
Overall, I like the song, but the use (misuse?) of that one word kind of ruins it for me. I have yet to read a convincing argument in defense of this adjective as an accurate, truthful descriptor for the love of God.
Anyway, here's a link to the article I mentioned earlier. This author says what I'm thinking better than I can say it.
Here's a link to the song if you're interested: https://www.youtube.com/watch?v=Sc6SSHuZvQE