^ They have TA’s (many of whom will go on to be profs at LACs). And TA’s would be at any mid-sized or larger Research U (both private and public), not just giant state flagships. BTW, this is where the grad school quality of a research U would matter as the better ones would get better TA’s as well.
Anyway, it depends on the resources of the LAC also. There are some with all of 2 CS profs. Their CS offerings would be limited, as you may gather.