I studied at Cambridge (which, btw, is definitely better than Oxford :-)).[1] Being in the Cambridge area when I got out of academia meant that there were plenty of jobs around that suited me. (Obviously that's a good thing in itself, but perhaps if I'd been somewhere else then I'd have moved to, say, London and had a different range of job opportunities.)

Pretty much every job I've taken I've found out about because someone at my new employer knew me. In some cases those were people who studied with me. Does that count as an effect of having been at a good university? I don't know -- if I'd been somewhere else, presumably other people would have known me, and maybe they'd have been even more impressed for want of strong competition :-). But there are lots of Cambridge people in Cambridge jobs, for obvious reasons.

The point here is that lots of things useful to my career have arisen from my having gone to a good university -- but not in the obvious way (people looking at my history and saying "oooh, Cambridge PhD, must be very smart").

[1] It occurs to me that there is a slight danger of that being taken more seriously than I intend it, so let me mention that Oxford and Cambridge are traditional rivals and that of course I would say Cambridge is obviously better. My actual opinion is that Cambridge is somewhat better for maths, science, technology, engineering, while Oxford is better for classics, history, politics, etc. If you want to be prime minister, go to Oxford. If you want to start a billion-dollar tech company, go to Cambridge. I'm not sure how they compare for intermediate fields like philosophy and law.