Yeah, thankfully this lab concept is absent, although it is always good to be advising grad students and postdocs. Most universities have tons of students who need to brush up on mediocre math backgrounds, which makes for a lot of paying work for math grad students.
It could be less in math because there isn't the same "lab" concept, where to be considered a "successful" professor you're supposed to oversee a lab of 3+ (better if it's 5+) PhD students, a post-doc or two, research scientists, etc.?