I believe the decision to run under the school's authority, or not, is a philosophical one; not a decision to be based solely on the $500 fee.
If your PTO is under the school's financial management, your money and organization is ultimately under the control of the school admin. It's possible that the admin could dictate how your group operates, how it spends and raises $, who makes decisions, who the officers are, etc. This type of parent group is like a committee of the school. You might have a great relationship with the current admin, and can't envision thte principal ever "taking over". But when your parent group is an extension of the school, the ultimate control is with the school. Many PTOs are comfortable with this model and make it work very well.
If your PTO sets itself up as a 501c3, non-profit group, independent of the school (like many, many other PTOs), your board of directors/officers and members dictate the policies of your organization. Your members decide how you'll raise $, how you'll spend it, and what events/projects you want to run. Obviously, all your work is done in cooperation with the school, but your members hold the final say. With this independence comes responsiblity to keep up with the requirements of the IRS (like filing the annual Form 990EZ), in order to retain the privilege and prestige of being a 501c3.
For a PTO with a $40,000 annual net income, you're a small business in the eyes of the IRS. Ethically, you have maybe 3 choices: run as a committee of the school and use their tax id number on your account; file for 501c3 status; acknowledge that your group is a small business and start paying federal taxes as necessary.
The $500 fee can be a show stopper, but there's more to consider than simply the cost of the application.