If you actually BUILT a character instead of choosing a body and class, I think youd find a lot more buy in for "who" you are even without a "This is what you were doing 5 days before this happened" hard tie-in.
Oh yah, I am always in favor of more character creation options. I am kind of disappointed that the backgrounds are so... Flaccid. They just give you skill proficiencies which while neat doesn't do much to really shape your character. Different backgrounds also infer abilities, tools, and other things based on what you picked. They should also definitely provide more dialogue options. If my character is a sailor I should have special dialogue concerning boats and the sea, as an example.
Also just more situations where an NPC asks you about your past with a few different options you can choose. Maybe even one or two race/class/background choices. It feels good to be made to think a little more about where my character came from even if it doesn't matter to the story.