The biggest advantage, as I see it, is that the effects of a successful economic attack are more widespread. So while throwing your bombers into battle at your front can help make that battle more decisive, throwing your bombers on a Strategic Bombing Run can impair the defender's ability to reinforce any other front on the map.
If, for example, you're strong on one front but one of your allies (or one of your other fronts) is being pummeled, a Strategic Bombing Run would let you take some heat off without (or in addition to) turning around and reinforcing it directly (which not only takes time, but also weakens your original line).
Yes, overwhelming your opponent can be a good tactic, but sometimes all you need to do is hold the line long enough for reinforcements to arrive, or for your allies to break through elsewhere. And if you can do that without committing (all of) your bombers to the battle, the territory-wide effects of a well-timed economic attack can be significant.
Europe during WW2 was not a one-front war. So when committing your bombers, just ask yourself how important any particular front is right now to the overall war.
(Full disclosure: I've played A&A, but never A&A:Europe in particular. Feel free to downvote me to oblivion if this post isn't actually useful and/or applicable.)