Tony Stark might have inherited and improved Howard Stark's with his state-of-the-art arc reactors and Iron Man suits, but Steve Rogers really honored the scientist's legacy with his accomplishments as Captain America. Howard Stark was, chronologically, one of the first characters to reveal that the MCU's version of Earth was far more advanced than real life. He developed impressive technological advancements such as flying cars, Captain America's vibranium shield, and the first attempts at clean, renewable energy through the Tesseract. Unfortunately, his career was cut short by Bucky Barnes a.k.a. the Winter Soldier on December 16, 1991, but not before creating the world's two greatest heroes.
Howard Stark saw Steve Rogers go from an ill and skinny recruit to the only perfect Super Soldier who managed to defeat Red Skull before disappearing in the Arctic Ocean. While looking for his body, Stark found the Tesseract and retrieved it in order to exploit its unlimited power. This was one of his favorite experiments, one which took him several years to research while he raised his son Tony. However, Howard never got to harness the power of the Tesseract or witness Tony become the world's (known) richest person, a warmonger, and the savior of the universe.
The first true step toward honoring Howard Stark's legacy in the MCU was in Iron Man's new arc reactor, which was precisely the source of power Howard Stark knew Tony would eventually refine. Tony's second arc reactor would be the gateway to increasingly complex inventions such as augmented reality and nanotechnology, but Steve Rogers utilized Howard Stark's experiments much more directly. Howard provided him with both the Super Soldier serum through Project Rebirth and the vibranium shield, the two only weapons Captain America used to become a legendary hero.
Howard Stark behaved like a mix between Tony Stark and Steve Rogers. Like Tony, he used his genius mind to develop ambitious technology and, consequently, instigate war. However, he used the world's only known reserves of vibranium to craft a defensive weapon. He might have planned for Captain America to be much more aggressive, but he still shared Cap's will to fight through preventive measures rather than Tony's characteristic hostility. Plus, Captain America kept Howard Stark's inventions until the end, contrary to Tony, who constantly manufactured his weapons with his own distinctive style.
It's uncharacteristic from Steve Rogers to forget Howard Stark after Howard Stark in 1970 during Avengers: Endgame's time heist. Howard Stark was key to the birth of Iron Man and Captain America — and therefore multiple other heroes such as War Machine and his own executioner, the Winter Soldier — but only Captain America preserved his military legacy.
