But that hasn't prevented them from trying to develop a young quarterback. This year, they brought in the latest in a series of hopefuls, adding Jordan Ta'amu from the XFL after the league went out of business and signing Michigan's Shea Patterson, who went undrafted.
It might seem odd for developmental quarterbacks to come to a team where the starter's job is occupied for the foreseeable future. But what the Chiefs lack in available playing time, they make up for as a good place to develop skills.
"One thing they'll have an opportunity to gain from being here is they'll get to learn a lot," offensive coordinator Eric Bieniemy said. "We have a very, very unique and diverse offense. On top of that, they get to watch how Pat Mahomes works as a professional. More importantly, they get an opportunity to work with a Chad Henne, who's been around a very, very long time and had provided some outstanding leadership qualities within that room."
The Chiefs have worked to develop low-round or undrafted quarterbacks ever since Andy Reid arrived as their coach in 2013. At least one developmental quarterback has been with the Chiefs each year, ranging from Tyler Bray and Aaron Murray in Reid's early seasons to Chase Litton and Kyle Shurmur more recently.
The Chiefs have yet to develop one into a productive NFL player, but they're trying again.
"It's an opportunity for him to make our football team," Reid said of Patterson. "That's how he has to look at it. It doesn't matter how you get in the door. You're in the door. Now, whatever you do with it, you do. You've got to handle yourself the right way and work with it. [Michigan coach] Jim Harbaugh spoke highly of him, and I trust Jim."
The top two spots on the Chiefs' quarterback depth chart are locked in with Mahomes and Henne. But there's room for the team to keep either Ta'amu or Patterson, at least on the practice squad, and it's not a stretch to think they could find a way to hold on to both.
Early in his college career at Ole Miss, before he transferred to Michigan, Patterson was thought to be a potential high-round draft pick. Ta'amu, who also played at Ole Miss, finished the brief XFL season third in passer rating and passing yards.
The Chiefs didn't offer Ta'amu a free-agent contract last year, when he went undrafted. But his few games for the St. Louis BattleHawks convinced them he was worth a look.
"It gave him an opportunity to get in there and compete and see what he can do," Reid said. "I think it will be interesting to watch him perform here.”
"The BattleHawks helped me a lot to showcase every talent I have and prove to everybody I can play," Ta'amu said. "The thing that scared most coaches is that I was young and didn't have much experience. The XFL helped me out a lot in getting that experience playing with a bunch of professional guys and showing that I can hang with the bigger guys and that I can move and throw and be accurate at the same time."
As for eventually getting to play, Ta'amu, 22, realizes he might have to move on to another team. But he indicated a starting job isn't the objective at this stage of his career.
"I feel like the Chiefs are in my alley, just the way the offense is and all of the great things I've been hearing about coach Reid and his offense and the quarterback room," he said. "Me and my agent kind of figured this would be the best opportunity for me to learn and keep growing. I'm such a young guy, so I'm always open to learn and kind of pick the quarterback room's brain, kind of pick Patrick and Henne's brain."