Yes and no. Here's why I think that anyway.
Firstly, as you said, university students are a dime a dozen. It is the generally accepted progression from high school these days. Years ago, most people would be doing trades and a very select few would go to university. I think now there is an emphasis from earlier generations to be degree qualified. The problem now is that since most - or a good proportion - of high school students progress to university, that degree qualified people are not uncommon.
Secondly, the problem with university students v trade qualified people is that generally trade qualified people are looked down upon nowadays in comparison to someone with an undergraduate degree. Therefore, there is a stigma associated with being a "dumb" tradesman. Also, the potential pay for a tradie is lower than a degree qualified person despite the fact they usually take the same time to do. Having being to university a long time ago, and also being a tradie myself (qualified chef), I find the difference staggering. A tradie usually has a lot more life experience, are a lot more practical and have a lot more common sense. However, a university graduate is generally a lot smarter, and seemingly clearer headed and a lot more focussed but don't have those skills that a tradie would have. I find university graduates to be like the "young child" and tradies to be like the "old head".
Thirdly, there is generally a lot more jobs available for a graduate in comparison to a tradesman. Unless you are in an industry where you are severely understaffed you are usually trying to hang on to a job. Just looking on Seek confirms this for me. Sure, there are trades that are in demand and will pay a lot. The mines for example. But eventually these will dry up. Traditionally, there has always been a big boom in resource production before a construction boom. Or on the other hand for graduates there is always boom industries. Take Information Technology for example. Ten years ago a new graduate could easily earn 75k+ within two years. Now you are lucky to make 55k.
Finally, as rx34 said, technology has facilitated the need for better qualified employees in industries where a trade is not suitable. Which I think will keep increasing over time. As more and more industries become technology focussed more and more people are going to need degrees. As well as technology there has always been those careers which have traditionally required qualifications. As the world get's bigger there will also be an increase in required graduates to fulfil these requirements.