Or is it not worth worrying about?
I think this ls very much down to the individual concerned!
This is how I would go about it;
Obviously where plants are growing it's better to hoe to avoid disturbing roots, .....is it best to leave them on the surface
In areas that are 'growing' as you put it, I tend to do both hand removal and hoeing.
That is; firstly I hoe between the rows and remove the debris with a rake.
Then I get down on my knees and go along the rows carefully removing as many of the weeds growing along the row as I can trying not to disturb what I am growing in the process.
but what about elsewhere?
I pulled and dug a lot of bindweed and couch - I was bringing the damp soil to the surface.
Do you mean where nothing is growing?
If so dig the area over, remove as much of the couch and bindweed as you can forget about exposing damp soil it will soon get wet again.