Totally, utterly disagree! I used to think exactly like this. I am from Norway and when I was young I was full of disdain for the Norwegian system, where government pays for all sorts of stuff. I was completely convinced like you that if only things were like in the US, where people have to pay lots of money to go to University, tell will be super serious students.
Then I went to the US to study....
Boy was I wrong!!! Having to pay for university had zero influence on the seriousness of the students I met. In fact I'd claim it was much worse than my experience from different European countries with free University.
What I realized is that if it is not government money it is going to be somebody elses money and that is frequently American parents. American students did not seem to be any more concerned about wasting their parents money than Norwegian students are concerned about wasting government money.
Again I think it is worse. Over the years, looking at this in more detail I think we are completely overestimating the effects of financial incentives. People are not really optimizing homo economicus. A lot of other factors matter equally much or more.
It is also about what society promotes and values. American society offers no respectable vocational training programs, and does not promote or value that path. Look at Switzerland and Germany which values this and provide great vocational schools. A lot more people go down that route and get skills to get well paid jobs without burying themselves in debt.
It is actually half decent in Norway as well since our system is closely modeled on the German system, however we have suffered from being too heavily influenced by the American view on education. Luckily there has been a push to change this and promote vocational training, causing more people to take that route.
However you can't get people in America to make sensible educational choices, when private schools are shamelessly misguiding student to reap more profits and society is pushing the idea that you can't make a good wage without going to college. Never mind the unhealthy American habit of thinking "anybody can be anything." American optimism can be great for launching google and facebook but it can be poisonous to people of average skill and talent who are deluded into thinking they can be anything they want as long as they work hard enough.
I think you got to work both on attitudes, what the school system offers, the values promoted. Financial incentives can be structured in many ways which doesn't need to punish people severely.
E.g. here in Norway you don't pay for school but you have living expenses, so you get a government loan and stipend to deal with that. As you pass classes they convert increasingly larger part of your student loans to grants. This gives a carrot to anybody to attempt to finish the study in reasonable time.