Shakespeare wrote the English of his time. Even for plays about Ancient Rome.

Tolkien didn’t really write the dialogue of his day. Not even the high literature type of dialogue of his day. It doesn’t mean his work is badly written, just that, indeed, his dialogue can be too stiff, much the way Icelandic Saga can do dialogue - which would sound very wooden to us, but we’d accept because in theory it’s best part isn’t the dialogue.