Sorry I'm just now seeing this.
The error 16 is caused by a security change on the phone. Sprint then sees the phone, but doesn't recognize it as having the ability to access its network, so you get error 16, or 67. In either error code you just call sprint and they reset your phone's security settings on their side, then send you a profile update to initialize your phone to their network and bam...back in business.
Now as to what causes it: It's likely that a similar exploit to the EVO3D was found in this phone, and, regardless of what the exploit was, that the secure areas were changed to handle the s-off setting. This doesn't seem to affect all phones (mine for example never had that problem) but does impact a significant number of them.
I said all that to say this: This zip does not touch any areas of your phone that do not directly affect a ROM. It wipes /boot /system /data /cache /devlog, and that's it. Any partitions affecting the physical hardware are left completely alone. That means that if you flash this wipe zip the only thing you have to do is install your new ROM and move on. Any issues with the phone at that point would be ROM or (more likely) Sprint network related.
Now that you know a whole lot more than you asked I'll shut up.
Sprint HTC ONE
Asus Eee Pad Transformer Prime
Asus Eee Pad Transformer
Previous Smart Phones:
HTC Evo 4G LTE
HTC Evo 4G
Touch Diamond (WinMO 6.5)