You know, it is entirely possible that in this scene, Steve feels the hammer shift…and stops straining. Maybe he knows that yes, he is worthy of Mjolnir, but doesn’t pick it up…
Because he doesn’t want or need the power the hammer can give him. He doesn’t want to rule Asgard. Being Captain America is enough.
Or because he knows that if he picks the hammer up, his friends will never see him the same way again. Steve has always been Captain America, the protector of the weak, the voice for those who can’t speak and the leader who sees his soldiers as friends. If he could wield Mjolnir he would be known as more than that. So much more. He would be able to bring down all the wrath of Asgard if he picked it up. But more importantly, his friends would look on him in awe, rather than as besties. They could never make conversation with him in the same way. Thor has always had the hammer, always been godly and noble, but if Steve, and only Steve, could pick up the hammer then they might resent him, might think that he’s better than them, Thor most of all. It would have started the Civil War earlier.
At heart Steve has always wanted peace, which was why he enlisted in the war. He wants to be with people who trust him and support him, and at the end of the day all he really needs is some time to kick back and have a chat with his friends and relax after a long day of being Captain America.
Things he’ll never have if everyone knew he could hold Thor’s hammer.