Is there a correlation between having a degree and competence? Because my experience is that there very much isn't.
I would go so far as to say that the information age has made educational material so widely and easily available that the only value universities provide is signaling and wealth/class filtering.
They certainly could. For instance, many of the still surviving bridges in Europe were built way before university degrees in architecture. I'll consider them cheaters because they didn't even attend a University! ;)
But there is another way to look at it: can all non-cheating students build bridges, design microprocessors or design rockets? I can give you an affirmative no.