The form attribute on fields is very useful to decouple the What from the How (it is laid out on the screen). You might for example want an upload widget, which does a separate request, right next to some other fields. Instead of wrapping things in forms (which you cannot nest) you can now freely lay out your document. Similarly you might want several fields or buttons spread across your document and don't want to wrap everything with a big form, or several forms.
I’ve been meaning to use these attributes for the very reasons you mention, but I’d need to check the impact on the accessibility tree. I’m not sure of the impact of having the submit buttons in a completely different part of the DOM to the inputs.
The accessibility tree doesn't represent form elements in relation to their particular <form>, a submit button's position in the accessibility tree will be equivalent to its position in the DOM tree.
The button's name (optionally also its description) and to some degree its position in the DOM order (what heading and/or other form elements precedes it) needs to be sufficient to convey what will happen when it's used.
