I can't speak specifically for the NFL, but this does actually happen regularly in a lot of leagues. Since the 2000s, Carlton and Adelaide in the AFL, as well as Melbourne Storm in the NRL, have both been punished for salary cap cheating in this form. The main thing stopping it is the punishment (Melbourne Storm were retroactively stripped of all of their premierships in that period and fined millions of dollars), which often far outweighs any advantages. For instance, Carlton were fined nearly a million dollars and stripped of all of their draft picks for two years, and then proceeded to be the worst team in the competition for most of that decade. The Adelaide Crows were fined nearly half a million dollars, were also stripped of two years of draft picks, lost arguably their best player in a trade to another team without receiving the compensation they otherwise would have, and had a number of players leave in quick succession, possibly due to the scandal. They went from being one of the best teams in the competition in 2012 to being a laughing stock.
Melbourne Storm, in the most infamous salary cap breach in Australian sporting history, had paid roughly $1,000,000 a year to their players outside of the cap, with "off the books" things like payments into offshore accounts, $20,000 gift cards, and boats. They were fined millions, had two of their premierships (and three minor premierships) removed, and were also stripped of their World Club Challenge champions title.
In short, yes, rorting the salary cap is very easy, and many people and many teams have done it. The thing stopping it from become extraordinarily common is that a sports club has so much scrutiny under it, and so many people who need to be kept quiet, and in the end, the punishment if you get caught means that it just isn't worth it.