Its just a detail, I don't care that much. But the MCU will always be more "realistic" if you will. So suddenly using the title "Captain America" on someone else would be weird imho
Its like if Tony dies and Rhodey starts to use his suit , he will never be Iron Man... he is Rhodey with Tony's suit. It would be weird to call him Iron Man
I'll give you that the MCU is at least different in that there are no secret identities. In the comics Captain America was always just that, a mystery man in a costume, so he could be anybody. But in the MCU the general population knows who he is and even gets history lessons if they don't. In fact, "Captain Rogers" is almost his default moniker.