Because some schools still heavily screen applicants prior to sending them applicants. And also, there is between a 10-20% attrition rate overall from applicants to send a primary to a school and those who never complete the essays. This is no different than people who ask why some schools want CASPer testing and others don't.
Admissions fees are not a cash cow for a university. In fact it doesn't even account for 1% of a universities revenue. Are they a bit higher than probably necessary? Maybe. Are they being greedy? No.
You use HMS as your reference. Last year they received 7900 applications. That means they had gross revenue of ~$900K. They employ 8 full-time staff with an average salary probably around $45K for the office workers and $100K for the Director positions. So you're probably looking at about $500K in total employee compensation. Then there is the food and amenities you receive if you interview. Then you have the annual licensing and maintenance fee associated with having an online admissions process and portal. Based on the school this could be anywhere from $50K-$150K depending on the implementation and additions to the base software a school requests. So right now, costs of handling the admissions process is somewhere between $600K and $700K. That's nearly 3/4th of the secondary revenue thy've received. That's excluding the mundane line item supplied that a department is responsible for - computers, printers, copiers, postage fees, customized letterhead paper, etc. Some schools, not sure about Harvard, financially compensate those faculty who serve on the admissions committee. It may be small, $5-6K/person a year, but there's another $40-50K, or 5% of their operating budget. So now we're up to potentially 80-85% of that $900K. Finally, this entire budget is based on a certain number of applicants, but if they get 500 less applicants than the year before, they run closer to operating in the red. So you can call admissions greedy, but it's not like at the end of the day they're rolling around in loads of cash they suckered you out of.