If it's not snug, your right, it'll free float, also known as rattle around.
Stuff that rattles around, vibrates.
More Vibration added to all the other stuff that's already happening to a barrel when a cartridge is fired and a bullet is launched can be detrimental when one seeks a "Harmonic Balance" to all the vibrations made.
It's pretty common knowledge that really accurate guns are "bedded" in the frame to lessen as much interference as possible of unknown or unwanted vibration and position changes.
I've personally found the same to be true with the Handi. We strive for the "lock-up" of the single break action to be the same each time we load, any small changes will change the barrel relation too the frame and change the point of impact. It may be small at say 100yrds, but exponentially more at 200 and beyond
A little time spent "bedding" the spacer firmly in a
proper and repeatable position in the forearm and against it's small contact area of the frame and near the chamber of the barrel has improved the accuracy in all my Handi rifles,, No wiggle at the forearm spacer equals tighter groups.
It works,, loose- don't work so good,,