FRANKFURT—The European Central Bank appears to be doing its part to help Greece reduce its crushing debt burden by transferring profits from its Greek bond holdings to euro-zone governments. There is just one problem: It remains far from clear that all this money will wind up in Athens.

By handing over its profits to national governments, the ECB is simply adhering to its long-standing rules. But it has no control over how Spain, Italy and others use their share of the billions they stand to gain from the ECB's €50 billion...