Knaidelach:
Indeed it seems many Chassidim did wear their Tallis Koton over their shirts, but all I’m saying is that a nice Svoroh isn’t necessarily the actual reason. It may very well be, but you haven’t brought anything convincing to make me believe it.
To reiterate, I think that most Lubavitchers would recognize that due to our (perhaps subconscious) way of thinking, we in a way find a untucked shirt to be more in line with the “Tziyur” of a real Chassid from Lubavitch, or Nevel, or perhaps Dokshitz. It very much goes with the Kasket, and the “L’chatchila Ariber” attitude in which we pride ourselves. This may make no sense to many readers, but I think this expresses the unspoken feelings of many Chassidim. Perhaps another Lubavitcher can back me up here.