How widespread is the use of "last author = teacher" on student papers?
As pointed out by others in the comments, this is very common in my field (Operations Research); at my institution this is the norm and is common in other disciplines.
A professor told me during my PhD that the marginal benefit of having their name first was small compared to having the student's name first.  Moreover, papers coming from a masters or PhD usually deserve to have the student's name first anyway.
I'm sure the community will have various opinions but I find this a good practice unless there's a clear contribution level issue.

Updates:
It is common to place students first then rest of contributors in alphabetical order. Further, as @BryanKrause points out (comment), it may be beneficial to not have your name first if it helps make the case you're capable of supervising the research process.