I doubt there would be a bowl effect from leaving the 6" by the trunk open.
I started with hard clay weeds and rubble and the rain would roll off if it in sheets.
After I added woodchips and autumn leaves rain soaks right in, even where there is no ground cover.
Now, I would say that most amendments are better off piled high rather than spread out.
After years of doing both, I prefer filling a two foot deep
raised bed with woodchips over spreading the same amount of woodchips 6" deep across the soil.
It's not about conserving woodchips, it's about conserving labor.
This doesn't really apply to trees, though I think a tree can really benefit from such raised bed nearby, seeing on it as a reservoir for nutrients soil and moisture.