[MC5C]

Not using the lower string bar has puts and takes. It somewhat radically changes the string break angle over the bridge, and really reduces the downforce on the bridge from the strings. You need a certain amount of bridge height so that the strings even touch the bridge saddles, so set up for the action height you want, measure the string height at the bridge and the string height at the tailpiece bar that the strings actually mount on. You'll get a good idea of what's what. My G6124 was retrofitted with a B6 Bigsby, which doesn't have the second string bar, and the bridge downforce was low enough that the floating bridge moved around really easily.

The big benefit of the single bar style Bigsby is that the tremelo action is really light, you can get roller or rocker bridges that let the strings move a bit, and it really can stay in tune very well indeed. But string height is critical. My 1962 G6124, being around 60 years old and starting to think it might need a neck reset, didn't have enough bridge height to make the B6 work properly so I put the stock tailpiece back on. When Gretsch chooses a tailpiece as a stock fitment on their guitars they think about things like bridge height and neck set, and choose the right one for that particular job.