Thanks for the input, nostalgicwisdom!
I’d like to clarify that when I said “math PhD”, I meant specifically math PhDs. Related fields like statistics, engineering or operations research accept students from a wider range of backgrounds.
On the upside, that means that attending a LAC doesn’t close very many doors early on. On the downside, the paths that do get trickier also tend to be the ones that are heavily promoted to the highest-achieving students.