Legacy check boxes are intended for use with [legacy] protection for filling in forms.

Try converting your form to Content Controls.

You can use Greg Maxey's add-in to assist with this. They are much more flexible and powerful and are intended for use with "No changes (Read only) protection.
Content Control Tools by Greg Maxey



The thing is, only filling in forms protection activates legacy checkboxes.


Create a Form Using Word Content Controls by Greg Maxey

Making Forms with Microsoft Word



Do not mix legacy controls and content controls in the same document.