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.
> 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.
"The purpose of this paper was a categorical settlement to the controversy surrounding the misconceptions involving the belief that data can be recovered following a wipe procedure. This study has demonstrated that correctly wiped data cannot reasonably be retrieved even if it is of a small size or found only over small parts of the hard drive. Not even with the use of a MFM or other known methods. The belief that a tool can be developed to retrieve gigabytes or terabytes of information from a wiped drive is in error."
Either way, both of those particular concerns are overkill for keeping a random thief from accessing your passwords.