Let's say I want to take down a Reinhardt shield (big, no crit-spot) and I'm at a distance outside of his melee range. I expect that I won't take it down in one barrel/volley, so I need to factor in reload time for multiple volleys.
The answer is right there in the information you link.
Assuming you're not so far away that you're experiencing damage fall-off and assuming all shots hit (such as shooting at Reinhardt's shield), you're doing 140 DPS with his left click. Factor in reload time (1.5s), and it's 420 damage over 4.5 seconds, or 93.33 DPS (86.667 against an armored target).
If you Fan the Hammer (and all shots hit), you're doing 270 DPS. Factor in reload time (which is the same, but you have to wait .3s after the animation to reload) and you're doing 96.4 DPS (85.7 against an armored target).
So, it looks like Fan the Hammer is marginally better against in armored targets if you're guaranteed to hit with all 6 shots. Miss even one and you're less efficient than LMB. Against an armored target it is about equal. This only makes it useful against can't-miss targets like point-blank tanks (if they already have some damage and you're attempting to finish them in one burst) or Reinhardt's shield.
Once you start to factor in things like crits, if you've got good aim left-mouse button almost certainly becomes better because FTH can't crit. Moreso if you factor in a smaller target that's hard to hit every shot with. I mean, even when I stun a Tracer or Genji at point-blank range, Fan the Hammer seems to miss about half the shots. I'm usually better off 2-tapping them with LMB, one of which can often be a headshot.
Fan the Hammer is really only worth it if you think you can land all the shots and crits aren't a factor, or if you think you can drop the target in a single burst. In my experience it's rare you'll actually land all the shots short of pumping them into a big tank at point blank range, which is not McCree's ideal engagement range or just popping Reinhardt's shield because you have nothing better to do. In most cases, though, you're better off left-clicking. Plus, a bonus of left-clicking Reinhardt is you can aim for the head, and if his shield happens to come down while you're firing, you can land a crit, whereas your FTH shot will probably miss entirely.