What would be the advantage of using an FYA in this situation over green arrows? Is it to give pedestrians the opportunity to cross?
The question is, how else can you do this safely. So let's again use the previous example I mentioned. A 4 way regular intersection where there are no turning restrictions. For the record, we shall decide to give NB an "extended green" or a "lagging left" to clear left turning traffic after the end of the through phase. (An "advanced green" or "leading left" does the opposite, it clears left turning traffic before the main through phase)
Now for the left turning traffic facing NB, we could use Signal Type 2 in this situation currently. This is a fully protected left turn, and with this comes the obvious disadvantage of potentially facing a total lack of oncoming traffic and not being allowed to turn. So using Signal Type 2, the NB-SB phase would run like this, if NB gets an extended green:
NB Left Signal | NB Main Signal | SB Main Signal |
Red Ball | Red Ball | Red Ball |
Red Ball | Green Ball | Green Ball |
Red Ball | Green Ball | Yellow Ball |
Red Ball | Green Ball | Red Ball |
Green Arrow | Green Ball | Red Ball |
Yellow Ball | Yellow Ball | Red Ball |
Red Ball | Red Ball | Red Ball |
As you can see, a lagging left can be created here. But as this a fully protected left turn signal, traffic won't be allowed to turn left AT ALL until the green arrow appears, which won't happen until the traffic facing SB gets a red (and some time for red clearance to protect left turners against red light runners).
So watch what happens if we try to use singal Type 9 or 10, in other words the protected-permissive signal, in this example, what appears in the table for "NB Left Signal" will be what appears in the arrow signal head at the bottom:
NB Left Signal | NB Main Signal | SB Main Signal |
| Red Ball | Red Ball |
| Green Ball | Green Ball |
| Green Ball | Yellow Ball YELLOW TRAP!! |
| Green Ball | Red Ball |
Green Arrow | Green Ball | Red Ball |
Yellow Arrow | Yellow Ball | Red Ball |
| Red Ball | Red Ball |
As we can see, as NB has the extended green, traffic turning left facing SB will get an early yellow while NB still faces a green. Causing what we all know as the yellow trap. A driver stuck in the intersection waiting to make a turn will not know the status of the oncoming through light, and thus it could be a good 15 seconds or more before the oncoming signal gets a yellow. There is also the more obvious issue of drivers not being aware that one side faces an extended green and thus a driver turning left assumes the car coming towards him is stopping when it isn't and this could lead to a jarring collision.
When we introduce FYA, we can do this safely, and here is how, the real disadvantage is that SB, although it gets no protected movements in this case will have to get a FYA signal as well.
NB Left Signal | NB Main Signal | SB Main Signal | SB Left Signal |
Red Arrow | Red Ball | Red Ball | Red Arrow |
FLASHING Yellow Arrow | Green Ball | Green Ball | FLASHING Yellow Arrow |
FLASHING Yellow Arrow | Green Ball | Yellow Ball | SOLID Yellow Arrow |
FLASHING Yellow Arrow | Green Ball | Red Ball | Red Arrow |
Green Arrow | Green Ball | Red Ball | Red Arrow |
SOLID Yellow Arrow | Yellow Ball | Red Ball | Red Arrow |
Red Arrow | Red Ball | Red Ball | Red Arrow |
And there we have it. In this case, NB turns can be made through the entire sequence as this is now a PPLT situation. SB traffic turning left WILL NOT get caught in a yellow trap now. Of course you can see the ambiguity I discussed on my other thread at play here, the solid yellow arrow, before all solid yellow arrows were protected, now in this case, SB's solid yellow arrow is actually a non protected yellow. That is the only real issue I have with the FYA signal myself.
EDIT!!
There is a yellow trap I missed in the first example involving SB traffic. It's getting late now and I'll correct it sometime tomorrow.
I'll ignore the first table for now since it still appears to have a yellow trap 
For the FYA, do drivers have to stay behind the stop line, or can they inch into the intersection like you would for a regular green light? I'm guessing you have to stay back, because otherwise it would appear to be another yellow trap.
Ok, in the first example, the only way I could eliminate the trap there would be to introduce a fully protected left turn for traffic facing the SB light. This fully protected signal could run concurrently with the NB left turn signal (in essence creating a simultaneous lagging turn) or a lead-lag protected turn situation, here SB gets their left turn at the beginning of the sequence, and NB gets their left turn at the end.
The first example is not really important for the issue at hand.
The yellow trap is a situation where suppose you are turning left, and you are in the intersection, you wait for a gap to make the turn, your light turns yellow, so you usually assume that oncoming traffic will come to a stop, but since oncoming traffic faces a green, they won't stop.
When FYA is added, the traffic heading SB that wants to turn left, who are yellow trapped normally won't be because there is now a dedicated signal for a left PERMISSIVE turn. Indeed, SB in our intersection never gets a protected phase for left turns.
When the solid yellow appears for SB (in this situation) this will mean that the oncoming traffic will face a yellow as well, and thus a driver won't be yellow trapped here.
Inching out into the intersection, that behavior will not change whatsoever, you would treat a FYA just as you would treat a green in a permissive turn situation, you wait for a gap and then move it.