I don’t think staying true to yourself is the same thing as not undergoing character development. And I don’t necessarily agree with either characterization.
In CA: First Avenger, Steve Rogers goes from a skinny kid on Brooklyn who wants more than anything to do his bit for a cause he believes in, to America’s bond drive mascot, to actually becoming a real leader rather just a figurehead, and then suddenly loses everyone he’s ever loved and becomes a Man Out of Time.
In CA: Winter Soldier, Steve Rogers starts the film as a company man, obeying orders because that’s what he’s used to, and ends up as a rebel bringing down the national security state. He also starts out the film as a Man Out of Time who doesn’t know how to adapt to civilian life or the present and ends the film as someone who’s made important friends – Nat and Sam – and has found a purpose in life (finding Bucky).
In CA: Civil War, Steve Rogers starts the film as an Avenger contentedly leading his team, and then has to choose between keeping his team together and doing what’s right, and then choosing between Tony and Bucky. By the end of the film, he’s lost Peggy Carter, he’s essentially resigned as Captain America by leaving the shield with Tony, his friendship with Tony is permanently damaged, Bucky has lost a limb and becomes a Popsicle, and he’s a wanted fugitive. And he’s now in a nascent relationship with Sharon Carter.
By contrast, I think Tony’s got some real issues with making permanent changes in his life – he built a bunch of weapons and then realized that was wrong, so he built some new ones and then realized that was wrong when his tech was turned against him, first by Obadiah Stane and then by Ivan Vanko. Then he built a bunch more and realized that was unhealthy and blew them all up in Iron Man 3. Then he went back on his promise and built a bunch more and built Ultron. He comes right out and says it in Civil War – he didn’t stop because he doesn’t want to stop.