I agree, employers tend not to care about which degree you got from a top university, as long as you got some degree from a brand name. And masters courses are

I agree, employers tend not to care about which degree you got from a top university, as long as you got some degree from a brand name. And masters courses are less competitive to get into. I teach at a large, well-known (in Europe), and decidedly mediocre university. I always get my top students into masters and PhD programmes at top universities where they then tend to do well. Mediocre universities often try their hardest to help their top students. I do this in parts because that's also my own trajectory: undergraduate at mediocre place, PhD at top school.