There was never a time when anyone had the option of requesting their role for Santa. At one point, Santa was told what role you wanted (though you were told what role to ask for in the PM). The Grinches had, at one point, the option to choose a role. I didn't give folks the chance to choose the role they wanted because the balancing act required would be a mess in a game like this. Note that the two times I did give 'choice' powers: I gave the mafia even STRONGER ones that made him nearly impossible to defeat (note that Vector died by a quirk added in to a role that was crazy for any townie to want to use), and in KotM which is a very different beast.
As for why the letter became standard: I realized, though, that it means that a group of people would know the role you COULD be. Nothing like having a pro-town player that can potentially know everyone's role.
The letter system wasn't MEANT to be used to crack the system. It was meant to be just a gimick in an otherwise standard game. You scumhunt.. look for people you believe are town, then send letters in the hopes of one of them being Santa. If enough townies did so (especially if Santa gave Coal to the mafia) then the town would have a good bit of power to use. Every role can show up twice! 2 redirectors, 2 cops, 2 doctors.. scum won't last. Now if the town can't read players well or become soo paranoid that they don't send letters...well.. you get a batch of 1 shots + a Princess to worry about...overall anti-town by my readings.
Along with that, the town has 3-5 days to scumhunt.. 5 days normally, 4 if santa is killed, and 3 if santa dies while Scrooge ends up a Mafia-ally.