Knowing what you have already tried is useful from a troubleshooting perspective...not to mention that if I suggest something you've already tried, it is wasted time on both our parts; mine for suggesting it and yours for waiting for me to make the redundant suggestion.
Many times there are multiple potential causes for an issue. Ruling out what has already been tried is what any competent troubleshooter is going to do.
Most of those "show your work" responses are designed purely to force the asker to prove that they have tried to solve the problem himself before asking Stack Overflow.
Showing your work can needlessly complicates the question, especially if it requires a lot of explanation. It's also irritating because someone knows the answer but is withholding it until you do what he wants.
I had that exact experience when I asked this question:
Right. The "show your work" stuff is about establishing a proof of work for effort expended on a question before anyone expends effort on an answer. It's a way of keeping the system honest, so askers aren't purely freeloading off answerers. It's a human blockchain!
Many times there are multiple potential causes for an issue. Ruling out what has already been tried is what any competent troubleshooter is going to do.