I have also being making some tests on fighting in loose formation, melee against melee, and have an initial impression that it can be beneficial for the player to fight this way in some cases.

I am not trying to make any crazy battle stratergies and am not a mad pro-loose guy but am rather trying to make the most out of my men in different situations, just thought you should know.

1-1 encounters always, always seem to benefit the loose formation. You don't seems to get much of a moral penalty. for fighting this way and get the extra flanking bonus and when fighting general units get to kill the general very early on, even if you don't want to change your line to loose, spread it out more so you wrap around the enemy unit, Moral penalty seems very low on this.
I have already mentioned the cavalry problems against loose, this I am always doing now, it is always better to change to loose against cavalry.

In bigger unit encounters I still cant say if its better or not.
I have tried it out in SP custom battles, historical battles (4 times) and in MP (3 times) and don't seems to get more or less of an advantage or disadvantage unless fighting against heavy cavalry armies or heavy archer armies.
In any case I think a player should be getting more of an moral penalty than what we are getting now. It doesnt seem natural for me to win the agincourt historical battle twice after changing my whole army to loose (minus the archers, only when needed to fight hand to hand) with very similar end results has in winning the "normal way" with the same tactics.