I played bluegrass banjo for many years, with my pinky anchored to the banjo head (never could get the ring finger to stay down, despite other recommendations about "greater stability", since I couldn't get the middle finger to move independently that way).
Also played flatpick guitar for a while, again with the pinky anchored.
When I took up mandolin, I decided to try keeping my right hand free. It has paid off I think because my hand is more relaxed, compared to how it used to be when I played guitar. So I'm perfectly happy to play "unanchored". It didn't take long to get used to it. The base of your right hand should have enough light contact with the strings, behind the bridge, that you don't feel lost.
The question comes up from time to time here, and some will argue it either way. -- Paul
He joyously felt himself idling, an unreflective mood in which water was water, sky was sky, breeze was breeze. He knew it couldn't last. -- Thomas McGuane, "Nothing but Blue Skies"