This topic will be discussed till the end of time. However, its fine to keep asking, new and experienced shooters will ask this question about the 1911 about the FLGR for a couple of reasons, i think.
First, you have the guys who say, "If John Moses Browning wanted a FLGR, he would have built it that way." or similar like comment. Well as much as admire JMB and his brilliance of design, without modern technology. He didn't design the 1911 with a lot of the features we add to the gun today. Ambisafeties, commander hammers, extended beavertails, sights! Just because JMB didn't design it, doesn't mean the weapon cant be enhanced upon.
THAT BEING SAID, does the FLGR enhance the design? my personal opinion is no it doesn't. I look at guys like Larry Vickers, Bill Wilson and Ken Hackathorn, for in my mind, these are the modern 1911 pistoleros advice that should be taken quite seriously. IF they dont feel the FLGR is necessary, and don't use one, it isnt. Now Wilson Combat sells FLGR's and you can add them but that is because they cater to buyers personal customization preference and that is a smart business move.
This gets confusing, because, we look at the competition circuit and pretty much most of those guys are running FLGRs, Travis Tomassie comes to mind. I have always felt these guys have erred on the side of better to have an not need, then need and not have. That seems to be a common thoughts process in the competition crowd. Does the FLGR provide extra benefit? maybe? Do I want to find out when I am attempting to shave every second possible? No.
Here is the thing I argue, learn to shoot what you bought, shoot it well. Then make changes, or sell it and get something else. The cost of adding a FLGR is better spent on more ammo. If your gun has one at purchase great, if it doesnt dont waste the money.
I have yet to see definitive engineering evidence that FLGR's enhance performance. I have seen a whole bunch of aftermarket parts cause problems, over travel screws in triggers being a big one. Thats my 2 Cents take it for it is worth.