Why? You would almost certainly get better data with higher reliability and no effort and no money spent from airplanes.live, adsbexchange.com, etc.
It's not something halfway critical to the operation–why would the FAA allow that? ADS-B Exchange is not run by volunteers–it's run by employees of JETNET LLC, an aviation intelligence company. Doing it yourself almost certainly gives you less information–you're not part of a global network of receivers. It almost certainly gives you less reliability–receivers in the big networks typically have a fair amount of overlap which gives redundancy your single receiver doesn't have.
It's also not FAA approved!