DS started demanding "proper" work at 3.5. Workbooks have been fabulous for us.
But I don't do corrections unless he asks for it, and he was only really able to understand what a correction like that would be like as he approached 5. Before that, if I did it, he absolutely hated it.
He far preferred me to just sit with him and listen to him as he worked things out, and prompt him in ways to work things out. And it's really helped him quite a bit. He knows how to work things out, talk things through.
The elementary school I went to had a "primary school". From 1-3 we weren't graded. It was brilliant. I actually went to 4th grade at a different school so I don't know how the transition was actually at that school, but for me it was just fine. I knew it was coming.
So to really do corrections on a 4 year old's paper just doesn't seem right. They are really just learning to learn, and anything else they learn at that point is bonus, IMO.
Now if she starts to WANT those corrections, do them, but do them gently and kindly. There's plenty of time for big x's in deep red ink later on.

DS knows he's facing more of that as we go into 1st grade work (as soon as I buy it! though this summer we're working on reading), especially since he really wants to work independently!
