Having started on the path of "bad storage" I'not sure it's a correct diagnosis. LE packages the userspace side of the OS into a single squashfs file (SYSTEM) which is decompressed into a virtual (read-only) filesystem in memory. This means that to successfully decompress the SYSTEM file we have to read all the data for SYSTEM from boot media. If there are bad blocks the decompression of SYSTEM and boot fails; LE is not the same as a conventional distro where a bad block impacts only the specific file(s) written on the bad block.
NB: As we decompress SYSTEM into RAM on systems with >=1GB RAM, you can get similar effects to bad boot media with bad RAM.
It's not clear what kind of hardware you're using, but I would deliberately unplug the SSD and boot from an LE image on SD/USB media to rule out RAM or boot media issues. Also, boot logs (dmesg) would be informative.