As an advisor, at what point do you decide that a PhD student no longer deserves authorship on a paper?
I am an associate professor who is very active in engineering research at a low-ranked R2 institution. Most non-top-10 institutions have a hard time attracting good PhD students, but here it is nearly impossible without deliberate, targeted recruiting. Consequently, I frequently find myself in the situation where I bring a student onto a project, only to find (sometimes a year or two later) that they are simply not up to doing the work. So, I do (or redo) all of the work myself and usually end up re-writing the entire paper. But even though I effectively did all the work, it was still a project assigned to a student, and worked on by a student for a considerable amount of time. So, in all of these cases, I left the student as the first author on the paper, with myself as last/corresponding author - even though the student's actual contribution was effectively nil.
This is not just me being non-confrontational or altruistic. As a faculty member, it is usually better to be last/corresponding author with a student as first author, than to be first author oneself. Student-first-author / advisor-last-author shows off mentoring ability as well as scientific contribution. So there's not much incentive to take the student off the author list, especially since doing so can make one come across as a greedy credit-grabbing advisor.
So my question is: at what point do I finally decide that a student no longer deserves first authorship? When I realize that I re-wrote the entire paper and generated all figures myself? When the student quits the program? When I learn that the student never did any work to begin with? When I learn that the student has not actually been dedicating the time to the project that was expected?
Or, is it better to err on the safe side, give away first authorship to undeserving students, and risk letting them take credit for something they did not earn?
Edit 1: In my field, the convention is that the first author is the primary contributor (usually a student or postdoc), the last & corresponding author is the senior lead, and the other authors are ordered roughly in accordance with contribution.
Edit 2: I am talking about removing as first author, not removing from the paper. Few students contribute little enough to warrant complete removal. However as far as how it looks, it looks equally bad (or even worse) to make myself first author, as it does to remove a student from a paper entirely.