I think that depends on the country and the type of uni. I have some friends that have been at top notch schools, and I have taken the time to see how they did things, and the trivium and quadrivium seem to be the cornerstones for elite education (which I was trying to self-replicate). That said, it feels like public schools (which are actually private... why this silly naming?) in the UK do this better than private ones, which is why in the UK you spend less time on those things in undergrad and above.
In the US I don't think they hardly reference the trivium or quadrivium, but the structure is loosely based on the principle, so because they have lost the reasoning behind it their course load is much more wild and varied, and sometimes unnecessary.
This is also my main beef with those who claim we should just do vocational training or very narrow course loads... the benefit of wide but shallow knowledge is large when applied properly. The US just doesn't apply it very properly. One thing the US does do much better, I must say, is the egalitarian culture though, which offers people the opportunity to laterally move in education much more freely.