There are certainly some complications that would come along with this, but there would be far fewer than with keeping a database of everyone who has ever applied for any job.
I don't love the idea, and I know quite a few people have tried making it work unsuccessfully, but I still think it's far more realistic.
But seriously, there is an equivalent strategy, and that is putting up a small road block such as writing a test application. The problem is that many qualified people won't do it. Those who are currently employed are the least motivated to pay in time or money to submit an application.
Either way, if you're trying to reduce the number of spam applications, this is certainly a great way of doing it, and it's much much simpler than building a massive database.
That said, it might be hard to figure out when hiring company has failed the applicant.
Stanford University, for example: $90 fee X 20,000 applicants = $1,800,000
I would have assumed that my universities' costs would be offset by the $40,000 I'm paying every year for the next four years, rather than erroneous fees that aren't tallied in the advertised total cost of attendance.
Basically, your tuition could be even higher if they dropped the fee to apply.