But I learned a long time ago that it's more important to simply
get the damned thing fixed. If that means shotgunning likely
components, so be it.

Would you be happy for a car mechanic to shotgun a fault on
your car, with you paying for his time and all the parts he is
unnecessarily fitting?

Yes, if an initial /conscientious/ troubleshoot didn't reveal the problem.
I'd rather pay for parts than time.

Of course, you can't draw an exact parallel between cars and electronic
equipment. It's easier to "see" what is wrong with mechanical devices, but
car parts tend to be more-expensive than electronic parts.