I am trying to think if I have ever stripped a fastener on a bike due to excess torque. I'm pretty sure the answer is no, never.
I am also trying to think if I have ever had a fastener come loose on a bike due to insufficient torque. I can only think of a couple of rack and fender bolts. And one quill bolt that I forgot to torque at all. I'm not counting 25.4 mm bars in 26 mm stems and weird mismatched stuff, or Wald baskets clamped to handlebars with crummy sheet metal straps.
Perhaps if I was working on CF bikes, I'd use a torque wrench. Or if I was working on other people's bikes for pay, and wanted an extra line of defense if my work was later questioned. But it would be just as easy to add a drop of blue LocTite.
Torque is not hard. 6 ftlb means applying 6 lb force at 1 foot from the fastener, or 12 lb at 6 inches. Lift a full milk jug, that is 8.5 lb. That amount of force will get you close enough.
For cars, the forces are much higher so a torque wrench makes more sense. Lug nuts at 55 ftlb, etc. I recall one suspension bolt that was spec'd at 250 ftlb. Ugh.
So is your question "Why should I use a torque wrench for bike work?" or "Why would anyone use a torque wrench for bike work?"
A lot of us have been answering the latter question, but you seem to actually mean the former. If you haven't needed to use one thus far, then don't. Congrats. It's simple.