My D has a handful of friends from HS who went to “non famous/non elite” small regional schools, that no one ever mentions on CC, for engineering. All three are gainfully employed and had no problems working in their fields (two mech es and one chem e).
My H’s last company actually switched recruiting strategies when he was there to stop going to the big name schools in the area, and focus on the regional programs (not necessary LACs but also the regional universities) because the kids at the big name schools were less likely to want to stay in the area, and were more interested in using the company as a stepping stone, vs making it their career. Also saved the company on relocation costs.