Not so much that it's not necessary...
I'm a couple years late to the party, but it might be worth pointing out that Apple (who has now entirely remove "Secure Erase" options from the Disk Utility app) hasn't really removed the option because it "isn't necessary" — according to its El Capitan security release notes, they did it because they can't guarantee a secure erase:
Description: An issue existed in guaranteeing secure deletion of Trash files on some systems, such as those with flash storage. This issue was addressed by removing the “Secure Empty Trash” option.
Glenn Fleishman, gives a good overview of this in "How to replace El Capitan's missing Secure Empty Trash." The fact that, currently, the only DoD/NSA approved SSD sanitation procedure is smelting or shredding the drive into a fine powder somewhat echoes the challenge in being able to wipe a drive, for sure.
It is pretty difficult to recover data from an SSD...
As Trane Francks explained, recovering data from an SSD is, by default, pretty difficult. The data isn't necessarily encrypted, but it is distributed data over many locations in order to perform as few writes as possible to a single location (both for performance and for drive longevity). So once data is deleted, find the place a file used to reside in is like putting together a multi-million piece jigsaw puzzle (all before any garbage collecting the drive may decide to do). It is possible to recover files from an SSD, but this usually requires a lot of extra effort.
To make it hard for recovery tools...
Encrypting a SSD with any kind of suitably secure key, and then erasing that key, makes it virtually impossible to recover any data. This can be done, on a Mac, by enabling FileVault, booting into recovery mode, unlocking and then deleting the drive with Disk Utility.
If you're just looking to make sure stuff is securely erased without nuking existing data, you could try using the diskutil terminal command — the command line version of DiskUtility, wherein secure erase options have not been removed:
sudo diskutil secureErase freespace 0 "/Volumes/[Disk Name]"
This should attempt to write and delete a couple tempfiles which will fill up the entire hard drive. In doing so, every available space should be filled and then cleared.
Good information on all these options can be found in "How to Securely Erase a Mac SSD".
Also, you can always try to run some data recovery tools to see if there is data that is still immediately available.
Based on that you are currently having a broken disk, I would strongly recommend stopping trying to mess more around and instead bite the bullet and reinstall MacOS
completely. After booting the installation media/recovery partition, start Disk Utility and use it to erase the drive completely, possibly even write a new partition layout and then install telling MacOS to use the whole drive.
If you have anything on it you want to keep, create a backup first (note 1). Time Machine is an obvious candidate as you can either get your home directory back, or you can tell the installer to restore your computer as it was. I did this a lot on my previous Mac after upgrading the harddrive. If you encrypt your backup, you get your passwords back too.
Note 1: I have been burned enough to never fiddle with disk partitions and file systems on machines without proper backup. You can literally lose everything in seconds. Messing with terminal commands is tempting fate :)
Best Answer
750 kB is so small, that this could easily be Spotlight indexing and other invisible files. Can you do Shift+Command+. in a Finder window of the empty disk to see hidden files? The original 20kB may have been a fluke before any of the files were added.
About the pictures, Disk Utility often doesn’t realize that the old partition has been deleted and shows 2 partitions that are each 2 TB (impossible). Restarting Disk Utility returns it to a normal state.