The Mac has passed the hardware diagnostics at the Apple Store multiple times. The components are unchanged from Yosemite, which did not have these issues. The OS has been freshly reinstalled, with the same problems.

This is also just one of a myriad of issues that have plagued the OS. Sierra has introduced me to new and wonderful ways to fail: http://i.imgur.com/HbVLWDq.png

If git is failing due to a system-wide file limit, that would explain why other programs are also failing. Perhaps some process has gone mad with creating files and if you find and delete those it will help things recover. (I agree with your general point -- just trying to be helpful in getting your computer back working.)

I reached the same conclusion, and the prime suspect in my investigations is Safari 10. However, once the system has hit the file limit, it never fully recovers without a reboot.

Google "too many open files" and you'll find posts about OS X but also Linux. Could it be git itself that's hitting a limit? Maybe you're hitting the shell's ulimit, not the system's per process or per-system open files max.

What year and ssd/hd?

I've had no problems except a couple programs that had broken features for a few weeks.