The NEA is not obliged to use their funds for improvements to institutions funded by taxes.
That they do is to their credit.
They spend their money, among other things, providing professional support and development to their members, which is not the same as "supporting public education". That's supporting the membership. And believe it or not, just like other organizations, they have to pay their employees. Journals don't publish themselves. Surveys are not self-compiling.
You don't think that the IRS would fall on them like a ton of bricks if they violated their tax status? They are not a PAC.