I have attended or participated in quite a few Ph.D. thesis defenses over the past few weeks, and in every case, the graduating Ph.D. student is going to a postdoc or short-term teaching position (e.g., sabbatical replacement). Our department has many recent graduates who are now in faculty positions at universities and colleges around the world, but almost none go directly from being students to being professors. I think that's a good thing overall for both the early-career scientist and the department, but it can be stressful for those with partners/spouses/children to move around so much and have the uncertainty about the future continue for the first few post-graduate years. Some choose to take a less desirable job right away rather than gamble with the uncertainty. I've seen some promising women scientists leave the research track for just that reason.
Only one graduate in the past 10 years from my research group is now a professor at a small liberal arts college, and that person attended a SLAC as an undergraduate. When I was in job-search mode, I got interviews at SLACs, as did my fellow job-seekers who had attended SLACs, but it was very rare for a SLAC to interview someone who had spent their entire career at large universities. Colleagues at small schools admit that they discriminate in this way because they think that someone who hasn't been part of the culture won't fit in or won't appreciate it. I don't think they would completely eliminate from consideration an otherwise excellent candidate, but having attended a SLAC gives one an edge for applying for faculty positions at one. I think this general approach filters out some excellent candidates who might have enjoyed a small liberal arts college experience but couldn't afford it or had other reasons (economic, family etc.) for attending a large university. An extreme example of this is one prominent SLAC whose department in my field consists almost entirely of faculty who attended that school as an undergraduate. At present, everyone in my research group (other than me) has been at medium to large universities for their entire academic careers and none of them are seriously considering faculty positions at small schools for reasons varying from lack of interest (wrong balance of teaching vs. research) to a strong feeling that they won't fit in. So, there's definitely some self-filtering at the application stage as well.
It can be a bit perilous to take a job at a SLAC (depending on the SLAC of course) if you have research aspirations beyond what can easily be accomplished at a small school, unless you don't stay there long (1-2 years, maybe 3 years max) and if you work insanely hard to do well at both teaching and research while you're there, despite having what is likely a huge teaching load and few research resources. That said, it is quite possible to develop an active research program by taking advantage of NSF and other programs that encourage research at undergraduate institutions.
8 years ago