In short, straight-arm FH opens up the limitations associated with different grips and increases overall power.
For conservative Eastern grips, it enables more natural forearm rotation, thereby increasing effective spin without giving up pace. For extreme grips, it increases your contact zone, enabling you to hit flat shots at waist or below level as well as your spinners at and above the shoulder level. In terms of overall power, it increases the effective line toward the ball, thereby enabling you to further accelerate the racquet and extend into the shot.
Naturally, it also have its disadvantages. It moves the contact zone further out. For somebody like Nadal, it's so far out that it's difficult for him to actually step into anything but a short ball. For somebody learning the WW FH, it reinforces very, very bad habits (especially overrotation of the torso), and can lead to somebody effectively screwing up their groundstroke. Once you can hit a WW FH in your sleep, it's a natural progression. Most people who use a straight-arm FH only use it to hit certain shots, and Federer himself doesn't use it as often as people assume. When he wants to hit an inside-out FH, he'll switch to a straight-arm, so that he can get the spin to pull down a wide angle. When he rallies CC shots with somebody else, he doesn't use it as much.
In terms of evolution, my impression is that straight-arm FH mostly arose from the Spanish variation of the FH (or what is taught in Spanish academies.) The trademark of the Spanish FH is a very, very heavy ball, whether it's a Nadal bouncer or a flatter Ferrero shot. There, they also emphasize more comeback strokes and emphasis on using extension through ball to generate most of pace. So, in that sense, the straight-arm variation is the logical extension of it.