The idea of letting Captain America holding the weapon that Thor was ‘worthy’ of has been suggested since ‘Age of Ultron’ during when Thor challenged everyone to lift the hammer up.
Vision was the second worthy being to be able to carry the hammer with ease. Cap was a man of justice and fairness – those personalities and values of him might just make him easily a worthy human of the hammer.
That’s as far as hammers are concerned.
Next thing we saw was Captain America slinging around the hammer AND sending lightning to his foes in ‘Endgame’. Wait, lightning?
Yes, Thor was the God of Thunder, no hammers. Thor typically channels his power to the hammer and then send a powerful shockwave to the floor or shoots in a linear projection. ‘Thor: Ragnarok’ confirms this as Thor summons the most powerful lightning with bare hands.
But, Odin forbids, Cap may have just turned himself into the god of Mjolnir with that.
Co-writer Christopher Marcus said, “There was certainly a debate at one point because particularly in Ragnarok, it establishes that Thor can summon the lightning without the hammer. I think Odin even says, ‘It was never the hammer.’ And yet Cap summons the lightning with the hammer. You get to those things and you’re like, ‘It’s too awesome not to do it! We’ll talk about it later,’”
Cap holding the hammer was a big moment and the whole theater, every time it screened, all over the world, erupted in cheers. Comic book fans are also not against it since the idea is canon and there are even more people who’ve held it. Jane Foster is next.
On the other hand, Odin also chanted the following words, “Whosoever holds this hammer, if he be worthy, shall possess the power of Thor.”