What do you mean, "introduced"?
Someone has to pay for the teaching in any case. Students paying for their education has been the default option since at least Bologna in 1088, when the studies happened because enough people wanted to pay for such an education. It has continued to be the case throughout history, except for some prestigious universities that got sponsored by wealthy rulers or religious studies that got sponsored by the church estates. It must be noted that this sponsorship shouldn't be considered "public education" but is rather analogous to various current stipends/grants/etc, since these were meant for a very small number of individuals, not as education for masses.
It's not that USA has "introduced tuition fees" - instead, some countries, like the Scandinavian countries mentioned, have comparably recently (historically speaking) introduced free higher education for everyone, but USA hasn't (yet?) introduced that.
Who are the actors here?
As for most questions about society, you can't really talk about "THE motivation for X" without being explicit about WHO has that motivation.
The core actor here is the people who actually decide on exact amounts of tuition, i.e., the people who manage the (often private) universities, not their students, faculty, parents or politicians. For them, there are at least four valid reasons for having tuition fees:
- That's income that they can use for whatever needs, so tuition is better than no tuition in that sense; even if they have other funding as well, most education institutions would prefer a larger budget;
- It filters out people based on their motivation - in any university setting, you don't want students who are "just visiting", as they disrupt the motivation and learning of others. Recent data from MOOCs with no barriers of entry show that this creates a large class of people who join just to try it out, since no real commitment of resources is required; that's okay for a MOOC, but disruptive in the 'classic' university environment, where you need to limit the number of students to whatever number you can afford do service properly.
- It filters out people based on their ability to pay - that's generally considered an inappropriate/illegal/evil goal nowadays, but back when the system was implemented, maintaining the separation of classes was an intentional goal (e.g. Numerus Clausus policies even in 20th century), not just a random byproduct of policies; your school and degree would have a better reputation if low-class "undesirables" would be kept out of the classrooms. A currently relevant argument is that diplomas are in some sense a Veblen good, where being affordable means less demand as you're believed to be cheap, thus automagically worse.
- They can't handle any sudden drops in income. Much of university expenses are fixed - building maintenance and tenured faculty won't become cheaper if you suddenly lose 20% of your income; so any cost reductions must be accompanied by a large influx of money (from whom?) or be a slow process of reducing volume - either teaching much less students, or doing much less to teach them.
There's no market pressure to reduce tuition
In a reasonable market there are downward pressures on price and demand - customer ability to pay and customer price sensitivity.
Recent changes in USA and some other education markets have greatly reduced those pressures.
The wide availability of student loans has resulted in a situation where people are buying education that they can't really afford - paying large amount of money (that they're borrowing) for even those education programs that won't actually have a "return on investment", while not having the spare resources to pay for it as a "hobby expense" for improving themselves. The impact of this is yet into the future, as student loans are maturing and the related bankruptcy cases are (and will be) rising.
And, more relevant to this question, student loans remove the visible difference between cheap and expensive university programs. Universities don't compete on price, since people don't choose them based on price. Some people do, but the majority of students don't think in a manner "oh, I can't afford a $40k tuition in a better university, so I'll apply only to $20k ones" in the same way as they would when purchasing, say, cars for the same amount; since the loans mask the direct impact on their daily budget. This means that universities have little motivation to lower their prices, as being cheaper won't gain them much, and being expensive doesn't restrict them from getting the good students they want, since the good students will get loans/stipends anyway.