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Literally yes, akshually.
"Worthy" by Asgardian standards requires adherence to a warrior code which Rogers meets. Pacifists, for example, can't lift it despite having a courage of their own
Steve knows what the cure for fascism is, and that's a large part of why he's worthy.
Only in End Game though. I think in Infinity Wars, he can kind of tilt it, which caught Thor by surprise.
I think you're thinking of age of ultron, and yea he makes it wiggle. Steve is also a pretty humble guy, so in theory he realized he could move it and then stopped to not show everyone up
Which makes sense because this mjolhir was from the past and didn't have knowledge the most recent current events.