Not testing doesn't solve anything. It might bring down the amount of players who are positive for covid, but it's not a productive move. These players have families, and parents. They deserve to know if they are carrying a deadly disease.
If they want to know, can they not take the tests on their own?
You analogy on the bills not existing because you don't check the mail is so faulty. The bills were never real, the risk to vaccinated players is near zero. They could spread it to others, but that's on them to take precautions knowing they are higher risk. Just like if you work in retail and 500 people come talk to you a day, you probably should take care before going to see grandma.
The players did the right thing, all but one getting vaccinated. That's good for the league and good for society. But where we fail as a society is when we say to people who got the vaccines you know we still don't trust you, we are going to subject you to more testing than almost anyone out there.
The only way to influence human behavior is use the carrot and stick principle. You get vaccinated, you get rewarded. They are taking those awards away now with the testing and these new rules for road trips. Those who go unvaccinated in society are getting treated far better than pro athletes all in the name of PR. I'm glad the NFL stepped up and said enough is enough on this.