I googled it and read the official Harvard application instructions, which specify the application fee is $75 although you can ask them to waive the fee. It didn't specify the odds of them granting the fee waiver (0%? 100%?) nor did it specify waiving would have no effect on your application (The same document specifically claimed in writing that the inability to schedule an interview has no negative effect on your application, but no such language WRT a fee waiver request). Also the risk was not specified, like if they deny and bill you will collections go after you or "merely" toss out your app for non-payment or ... The problem is not so much $75, as the general cultural advice to apply to 10 other schools just in case which turns it into a $750 problem for a kid.

They also want a rather remarkable amount of (expensive) paperwork sent to them. Everything about the SAT costs money, $50 for the basic test, $11 to send the scores to a school (seriously, $11? In 2013 it costs $11 to shove some digits somewhere?) although all is peppered with "fee waiver available".

Aside from the cost investment, there is also the time investment problem. As per above if you decide you can't afford it, and they want a fairly large amount of work done to apply, even if even more paperwork could result in it being free, well, why bother?