You don't get a lawyer to carry the ball, and you don't get a football player to draft a contract. They are professionals in their fields for a reason.
buybuydandavis brings up an interesting point about how agents don't always align 100% with their players, but the track record of players signing their own contracts is pretty dismal. Russell Okung I remember tried this with the Chargers (Broncos? I forget), and ended up signing a 4 year deal that had 3 voidable years on it. IIRC, he got hurt in his first season, and you can guess what happened after that.
Richard Sherman signed a $30M contract with $3M guaranteed. He was coming off an Achilles injury, but still, that guaranteed offer is insultingly low - SF probably wouldn't have even tried to offer that contract if Sherman had an agent attached. Sherman won that bet and is about to collect every penny of that contract with the 49ers (which almost
never happens) without splitting anything with an agent. He was on social media gloating about it, and I guess he's in his right to after it worked for him, but it was more of a bad contract that he just lucked out on.
Long story short, you hire an agent and you give him his 3%, because odds are he'll end up earning you more than that.
On a side note, I remember reading this piece written by Richard Sherman talking about his contract negotiations with Seattle (although I get the feeling that TPT ghostwrites/edits their players' articles... every NFL player on there seems to write with the same voice). Sherman gets that "thug" reputation in the media, as he once notably described it, but he's actually a pretty smart guy.
https://www.theplayerstribune.com/en-us/articles/richard-sherman-49ers-seahawks-free-agency
Found this article too while I was searching for TPT post above, this one is good as well.
https://www.cnbc.com/2019/02/01/why-nfl-star-richard-sherman-drove-a-dodge-challenger.html