Is this the same as "Let me know if you have any questions."?
I often end emails like this, more as an acknowledgement that while I feel that I am clear, it may not seem clear to you, and to not hesitate to come back to me if anything is not clear to you.
But maybe this also is leaving a similar impression as "Let me know how I can help."?
After a support session I usually end with "Let me know if you run into any issues."
I do frequently wonder if that's the best way to end the email... as what I want to suggest is "Email me back directly if something happens, but I don't think anything will."
Maybe: "Feel free to ping me directly if you run into any issues."
It's not exactly the same, assuming you've already proposed a solution in the email, but it is still kind of redundant to say. I think most clients will let you know if they have a question, regardless if you write that.
If you think they might have questions, why not anticipate a question and answer it in the email?
I also feel it's technically redundant -- like you said, they will follow up regardless -- but I think I do it to just give a more inviting tone/closing to the email.
However, I also used to end all of my StackOverflow questions with "Thanks in advance." just to be polite and appreciative to those spending their time reading/responding to my questions, until it kept getting edited out (for the same reason, redundant noise), so I got the hint and stopped.
About StackOverflow, it's probably because questions there are not supposed to be like a forum (as in, someone has a problem and wants a solution), but more like future reference for anyone searching for that. So they remove stuff that sounds more personal. That's my guess.
I often end emails like this, more as an acknowledgement that while I feel that I am clear, it may not seem clear to you, and to not hesitate to come back to me if anything is not clear to you.
But maybe this also is leaving a similar impression as "Let me know how I can help."?