It would be mighty inconvenient.
It's definitely difficult to write about a character with god-like powers. Just like Superman has kryptonite, Thor needs to be worthy in order to wield his hammer and be the all-powerful hero we love. It's happened in the comics more than once, and Thor spent a lot of his first solo movie wandering around Earth without his super-strength.
Could it happen again in the MCU?
Perhaps during Ragnarok? It's not a matter of 'what could go wrong' so much as 'how many things are definitely going to go wrong'... what do you think?