Years ago we settled on using block device encryption for all flash storage and then destroying the headers or revoking all keys.

This satisfies the infeasibility requirement of NIST SP 800-88 without relying on flash vendors to have appropriately implemented ATA command standards like secure erase, which almost none fully do.

This destroys the filesystem, but not the physical disk, right? I mean, will the SSD be usable after that, albeit, by installing a new filesystem and reformatting?

Correct. It's not like when degaussing wipes the track information from a HDD.

This is also as opposed to relying on the self-encrypting feature on most modern flash. Whether you're dealing with high enough asset value to warrant this level of interest or are just beholden to the same standards, you should reach out to your flash vendor for clarification.

No OS handling sensitive data should ever save on unencrypted volumes, ever. Particularly nowadays - with BitLocker and FileVault it’s trivial to achieve this even on desktops and laptops. When you want to kill the data, you just destroy the/any key and you’re done.

Why rely on hardware encryption, when software encryption is basically free?

I guess a hammer takes care of that too :)