Now, he must do more.
The veteran quarterback with a reputation for being a game manager is being called upon to build on a solid if unremarkable season.
After signing a four-year, $68 million extension before training camp, Smith proceeded to throw for more than 3,000 yards and 18 touchdowns with only six interceptions, despite having his season cut a game short by injury.
But if the Chiefs hope to return to the playoffs - and win their first postseason game since 1993 - it will almost certainly be because their passing game flourishes this season.
''I feel really good,'' said Smith, who is entering his 10th season in the league. ''It's a point of emphasis for us all offseason. We worked hard on it, QBs and wideouts included. We worked really hard on it and I do feel good with where we're at.''
Much of his career, Smith has been hampered by spotty options at wide receiver. Dwayne Bowe and Donnie Avery hardly fit Chiefs coach Andy Reid's offense, but other than a host of also-rans, they were just about all Smith had at his disposal.
That is hardly the case this season.
The Chiefs signed Jeremy Maclin, who grew up in Reid's offense in Philadelphia - although the high-profile free agent missed Monday's practice with an injury.
They also drafted Chris Conley in the third round, and the speedy, rangy pass-catcher out of Georgia returned to the practice field Monday for the first time since July 29 after dealing with a knee injury.
Throw in the emergence of tight end Travis Kelce as a bona fide star last season, and running back Jamaal Charles's ability to catch passes out of the backfield, and Smith has more weapons in the huddle than any other time in his first two years in Kansas City.
He also has more down-the-field options.
One of the big criticisms of Smith has been his reluctance to throw deep, which might help loosen up opposing defenses and give Charles room to run. Smith completed just 40 passes of at least 20 yards last season, ranking in the bottom half of NFL starters, and three of at least 40 yards - tied for 35th among all quarterbacks that attempted a pass.
''Your percentages obviously go down when you shoot deep as opposed to short and intermediate passes, that only makes sense,'' Reid said. ''But he's connected on some nice ones (in practice).
Even offensive coordinator Doug Pederson, himself a former quarterback, seems to be hoping Smith takes more chances, at least before the games start to count.
''If you're going to throw an interception, training camp is the time to throw it. Let's test our skill and ability, let's see what our guys can do,'' Pederson said.
''Let's see what the quarterback can do, let's see what our receivers can do. This is the time to test that, and we've got all of the confidence in the world, as a staff, when we call those plays that they're completion plays and that Alex will do the right thing with the ball.''
Smith and his wide receivers are only part of the equation, though. To make the passing game click, the offensive line must protect better than it did last season, when it allowed Smith to get sacked a career-high 45 times in just 15 games.
So far, the Chiefs have yet to settle on a front five. Rookie center Mitch Morse is in a tight competition with Eric Kush, and the entire right side of the line remains in flux with Jeff Allen, Paul Fanaika and Donald Stephenson among those playing musical chairs.
''It doesn't matter if you have two or three studs,'' Allen said, ''you have to have five guys working together. That is what we're trying to get.''
Nobody would be happier to see that than Smith, who understands the burden of a successful season could very well fall on his right shoulder.
''I really feel that we have a lot of the pieces that it takes,'' he said. ''You just never know how long those windows last and you have to make the most out of this opportunity, and I really do think we have an opportunity in front of us.''
NOTES: Maclin woke up Monday with a strained neck. X-rays were negative. ''Everything is OK. We just have to get the spasm out of it,'' Reid said. ''I'm not sure exactly when it happened.'' It is unclear whether Maclin will play in Saturday's preseason opener at Arizona. ... OLB Dee Ford remained out of practice after going through the concussion protocol this past weekend.
AP NFL website: www.pro32.ap.org and www.twitter.com/AP-NFL