With wear leveling and modern filesystems, it's harder than that actually overwrite the file on disk (for modern definitions of the word disk). The operating system will ask the storage device to delete the data, but there aren't actually guarantees that the storage device actually listened to the operating system's request to delete the data.
Which is why if you care about sensitive data not being recoverable from failed media (eq. banking database, PII, mediacal records, etc.) you should always use full disk encryption (LUKS, bitkeeper, veracrypt, etc.).
That way anything one could recover from that device afterwards would be effectively random noise to them without the decryption key, regardless how the firmware of the device actually wrote the individual data blocks.
