Well, the historical bases for this house rule were:
A) The UK attacks on Vichy French ships in 1940, and
B) The German attacks on Italian army units in 1943.
In both cases, the fall of a capital (Paris, then Rome) precipitated a political polarization of the remaining forces, and nations were forced to attack former allies in order to preserve their positions. At the same time as some portions of the military switched to the other side, other elements decided to keep the fight going, on the same side as their previous alignment. There was a lot of confusion, and opportunism, and this is not modeled in the A&A game out-of-the-box; however, I think that by employing the pro-Axis and pro-Allied neutral rules, this effect can be easily simulated.
I think that if London, or Moscow, or Washington, or Berlin fell, the same process would occur for those great powers in the chaos that followed… Thus, I advise the application of this house rule when ANY capital falls. This shows the great importance of the capitals and the severe disruption that results when they are captured. It should also make the game go a great deal faster, as when a nation is beheaded, roughly half of its territories will immediately be gobbled up by its former enemies, or preemptively attacked by its former allies. This is not necessarily a bad thing, as it will lead to very interesting new possibilities and challenges for all players.
The rule has not yet been play-tested, but it’s intuitive enough that you can see the effect it will have on the game. Capitals don’t fall that often, and when they do it’s often late in the game and decisive. Therefore, the cases where these rules will pop up the most is with France and Italy, the powers that are most likely to go out earliest in the game, and whose downfall doesn’t necessarily mean the end of the war for their allies…
The fantasy scenario for the German player is getting the result of a pro-Axis Vichy French fleet in the Mediterranean… one the Italians could annex, or the British would be obliged to scupper. The fantasy scenario for the US player is getting a Co-Belligerent Italian army in Africa or the Middle East, to save the long trip back to America for fresh troops to transport.