Per your security concerns, yeah it would be overkill. What they are attempting to protect is two fold, information leakage about how much data is available (size of non-zero data, even if encrypted) and trying to ensure previously deleted data is harder to pull from the magnetic field. On the second point, it is possible to extract previously written data even if it has been overwritten with disassembly of the harddrive and speacial tools. This is why things like Boot and nuke exist and why the DoD requires harddrives be physically destroyed by incineration rather than reused.

Either way, both of those particular concerns are overkill for keeping a random thief from accessing your passwords.