Sam Wilson (Anthony Mackie) may be Captain America and a noble one at that, but he's lying to himself about one thing—he's not strong enough the way he is. Brave New World offered multiple situations where a super soldier serum would've come in handy, and Cap felt the reality of the situation before the movie's end.
Throughout the film, Wilson gets outclassed over and over again. He gets cornered by a heavy mercenary who has about fifty pounds on him, narrowly escaping with his life. In another situation, a group of armed guards subdue him, proving that the vibranium wings make a difference. And then there's the Red Hulk fight.

All the buildups to Brave New World suggested that Cap's vibranium suit would give Red Hulk a challenge, except it proved ineffective. Red Hulk ripped Cap's helmet off his head in one exchange, smashed the jet boosters on his back during another, pulled a wing directly off the suit towards the end of the fight, and barely took a fall after Sam hit him with a kinetically charged strike from the remaining wingtip.
Wilson only managed to bring Ross down by talking him down, which was quick-fix for a scene inching toward Cap dying. Because, had the Red Hulk continued rampaging, that would've been the end for Sam Wilson.
The issue with Brave New World is that the crux of the film was ineffective. While establishing Wilson as a different kind of Captain America sounds good, the scenarios presented in Brave New World reinforce how super strength and healing would level the playing field. Wilson even jokes that he "should've taken the serum" several times in the film. It goes to show that he made a mistake.

Having Wilson believe that he can continue soldiering without an upgrade is asking to make him a martyr. The Leader (Time Blake Nelson) hinted at the multiversal incursions on their way, throwing new variables into the mix. Any variant with god-like power is also an immediate threat to human-level heroes such as Captain America. Unless, however, Wilson accepts the truth.
After feeling the struggle to merely survive, he might have to seek out a serum. Red Hulk literally ripped the wings off his back; Wilson won't forget that easily. He also witnessed another gamma monster shrug off a kinetic blast that would normally kill its target. Then, learning that stronger beings are entering their universe will put real fear into him.
A Way Forward

The solution for Sam's dilemma has been present for a while: Isaiah Bradley (Carl Lumbly). The formerly imprisoned Captain America possesses blood that can grant Wilson superhuman strength, durability, and accelerated healing. Bradley hasn't offered it to him, but after Wilson freed him from prison, the veteran hero might want to show his gratitude. There's also a precedent for Bradley showing generosity in the source material.
In the comics, Bradley transfuses his blood into Eli Bradley after the latter is in a grave accident. The subsequent transfusion grants Eli a fraction of his grandfather's powers. He then goes on to co-lead the Young Avengers.
The comics pertain to Wilson since he could be on the receiving end of the blood transfusion instead of Eli Bradley. Cap needs it more, and there hasn't been much sign of Eli lately, either. He's presumably a member of the upcoming team of teens, but in Cap's world, he's virtually nonexistent.
Granting Wilson a boost is necessary and apt for the coming events. Both Doomsday and Secret Wars movies warrant the MCU's heroes to be the best versions of themselves. So, whether Sam Wilson wants to take a super soldier serum or not, accepting one may be necessary for survival.
Captain America: Brave New World is currently in theaters around the world.