The coax feed is unbalanced. The inverted-L is unbalanced. What does a 1:1 balun accomplish? A choke balun might keep RF off the outside of the coax feedline if your radials aren't providing an effective RF ground - but that means you have loss in the ground system.
You can still have common mode current on the feedline even when the ground system
has insignificant loss: an elevated ground plane for VHF, for example, has very little loss
in the radials, but they still may not be sufficient to keep the outside of the coax from
acting like one of the radials.
So a 1 : 1 current balun ( = choke balun ) may help to reduce the receive noise level by
providing better decoupling of the feedline in some cases. A voltage balun, however,
would be a poor choice in this application because both the feedline and the load are
unbalanced: impressing equal voltages on ground and the antenna probably willforce
common mode currents on the coax.