It is surprisingly difficult to ensure deliberate data loss
This can be the case for something like an ATA Secure Erase command, which is why the Sanitize commands were introduced to ATA, SCSI and NVMe. Those do explicitly mandate that all user data be erased, including from all caches and any storage media that is not normally accessible to the host system (ie. old blocks that haven't been garbage collected yet).
2) While it's been "common knowledge" since Gutmann that data from old writes can be recovered (thus the advice to write multiple passes of random data), this turns out to have been iffy in Gutmann's day and an outright myth today. Multiple university teams have tried and failed to recover data using advanced techniques (such as SEM tomography) after a single zero pass. Generally the success rate for single bits is only slightly better than random chance. Gutmann himself criticized multi-pass overwriting as "a kind of voodoo incantation to banish evil spirits" and unnecessary today.
3) By far the larger concern in data recovery, for platters as well as SSDs, is caches and remapping performed in the firmware. As a result, the ATA secure erase command is the best way to destroy data because it allows the controller to employ its special knowledge of the architecture of the drive. However, ATA SE has been found to be extremely inconsistently implemented, especially on consumer hard drives. The inability to reliably verify good completion of the ATA SE is a major contributor towards preference for "self-encrypting" drives in which ATA SE can be reliably achieved by clearing the internal crypto information, and the US government's recommendation that drives can only reliably be cleared by physical destruction. Physical destruction is probably your best bet as well, because self-encrypting enterprise drives come at a substantial price premium and you still lack insight into the quality of their firmware. In other words, the price of a drive with an assured good ATA SE implementation is probably higher than the price of a cheap drive and the one you'll replace it with after you crush it.
It's true that multiple overwrites are overkill. But for SSD's it's has been shown that it's possible to read data after a full overwrite [1].
[1] https://static.usenix.org/event/fast11/tech/full_papers/Wei....
There is a potential benefit to multi-pass random write to SSDs in this case, but this paper shows exactly why you shouldn't do this: because the improvement in security from random overwrites is stochastic at best and cannot be guaranteed without full knowledge of the behavior of the controller, as can be seen in the paper in the drives which continued to contain remnant data after many passes.
As the paper finds, multi-pass overwrite is not a valid technique to sanitize SSDs, and is still cargo-cult security.