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?
All excellent points. My understanding is that fee waivers are granted more or less automatically for any plausible candidate, and no school would ever take anyone to collections over a denied fee waiver request (they just wouldn't process the application until the fee is paid), but as you point out, low-income / first-generation-college applicants are unlikely to know this stuff. There are also programs like QuestBridge which attempt to streamline the process of applying to multiple schools, fee waivers, etc., but again a lot of students don't know about them.
My brother went to Harvard, partly because their financial aid offer was best, and I recall my father cursing the required forms. He's a lawyer, so ordinary legalese doesn't phase him, but he found those troublesome. Now I imagine a family without a JD in it, or even without a BA in it, trying to fill them out...
I'll toss in that when price discrimination (which is what selectively subsidized education essentially is) has a time component, the lowest-income potential students are least likely to be able to take advantage of it, being short on both time and money. Higher income families have access to both more free time (especially in our leisure-consumption society) and better access to knowledge (including buying it, e.g. test-prep or better school councilors).