A couple of things to note:
Scholarship dollars at private schools are 'soft' dollars, meaning there is no hard currency spent. Tuition and fees are hard dollars.
Overhead for upkeep of most 'track' facilities is not really a factor. There is some for sure, but much of it would be done for football/lacrosse/soccer/recreation use anyway
Look there are many opinions on this topic and all may be correct on an institution by institution basis. Many factors, many situation across DII.
Here's the real question: How do we justify Track and Field on the DII level? Outstanding student experience creates better alumni and future support? Great learning gains take place at practice and competitions? Let's hear why schools should sponsor Track in the first place. Many opinions on this as well.
I will end with this. Many private schools have track (and other sports) to attract students (fill beds and desks). I believe many make money on the tuition/expense equation...but that does not mean Track is done right, or well, or even creates good experiences for students.