One possible relevant benefit of free college, though, is that it removes a lot of the bad incentives in the university-student relationship. If students aren't in the paying customer role, and universities aren't so strongly incentivized to sell as many degrees as possible, it's a lot easier to enforce strict academic standards. So it could actually improve the degree inflation situation.
But all in all, I think it worked out pretty well in the past - no tuition, free access and lectures are public anyway. So everyone gets a chance to try it, most drop out in the first year, probably changing field of study once or twice. But as we don't have that minor/major stuff but the curricula are extremely specialized, this is probably not bad for widening the horizon. Still better than arbitrary tests or the weird numerus clausus in Germany.
I don't think that an university degree should be mandatory for everyone (we have a lot of specialized schools as an alternative), but it's good if the option to try it is there.
Let's not paint with too-broad a brush here. If the "exam bank" of possible test questions is sufficiently comprehensive and rigorous, then teaching to the test is not a joke at all, but an effective pedagogical method. If students can write acceptable answers to a random selection of questions from such an exam bank, it follows that those students do indeed know what you want them to know, at least to the extent that testing can ascertain whether or not that's the case.