To answer your question , Nameless, From what i have heard, it’s because the CHosson and Kallah dance together holding hands,and one may not show “chiba berabim”. For this reason, most Litvish/yeshiva people do not hold hands coming off from the chupa, or coming in to dancing either. Another svara might be that since there are times when this would not be possible (chupas nidda) it may be worthwhile to abolish the custom for everyone so as not to shame the chosson and kallah or make it obvious.. (we have other cases where we have abolished a minhag so as not to embarrass people , such as reading from the Torah.)
Those that do do these things obviously have a reason to say why holding hands in public, which is normally inapproprate (assur) is fine then. About holding hands between the chuppa and yichud room, I have heard it is because there shouldn’t be a hefsek to both parts of the kiddushin.