First, Cage was created in the comics when an experiment was tested on inmates. He became strong and bullet proof.
Willis planted drugs in Lucas' Harlem apartment and tipped off the cops. Lucas is then wrongly convicted and imprisoned. Lucas then volunteers for an experiment which will shorten his sentence. Dr. Noah Burstein puts Lucas in an electrical field with a chemical compound, leaving him unattended for a moment. Rackham tampers with the controls, causing an overload. Pushed way past its original intent, the resulting incident empowers Lucas with super strength and gives him nearly impervious skin. Lucas uses his power to escape from the prison and later makes his way back to New York City.
The idea isn't that he is better than Captain America, Cap has the training, but more importantly the character/ the heart. His personality is different. He is more selfless, not that Cage is a bad guy, but he is a different person that Cap. He decided to use his powers to get money in the Heroes for Hire. He is also a little angrier and less patient, and not a strategist with military training, and hasn't been through WWII.
The idea is already on its way, Red Skull was the 1st Super Soldier, but it didn't work exactly. Zemo experimented with his version of the Super Soldier Serum on Bucky, which will be explored in Cap 2 with the Winter Soldier. Ross used the serum on Blonsky and made him the Abomination. Banner told Cap in the Avengers that he becomes the Hulk as a result of experimenting with the Super Soldier Serum. So in effect Hulk > Captain America.
This would just go along with the Ultimate comics idea that many characters powers can be traced back to the Soldier Soldier Experiment Race, like there was the Moon Race and the Nuclear Power Race in real life. In the Marvel movie universe there could be the Super Soldier Race.
In would be a similar idea to Stark's arc reactor being traced back to the cosmic cube which came from Thor's Asgard. So Stark's repulsar Blasts and arc reactor can be connected to Thor. Connecting a few Marvel characters to Cap would help. (Just like I think Black Widow's stingers should be traced back to Pym and Wasp's Stingers.)
Cage would be, like Cap and like Hulk and like Blonsky, another unexpected, and unrecreatable result. They didn't expect him to become like he did, but then they also couldn't control him. And they can't make another one of him. But it also bridges the gap between Hulk and Cap, why did Hulk become so different than Cap? Well, maybe not so different if Cage is similar to both.
For anyone worried that Cage is more powerful than Captain America and Cap would be a Joke, no he wouldn't.
Cap, in hand to hand combat, might beat Cage. He has the training, the skills, the shield, the heart. etc. But also Thor is stronger than Captain America and so is the Hulk.
And anyway, it just an idea. A way to bring in Cage, and his origin, while still trying him into the Marvel universe without making it expand too much, keeping it small and connected and stuff.