I guess y'all have some magical undershirts.
At best an undershirt will delay transfer, which is a fine thing. And of course there's that snazzy Don-Draper American-cravat look.
I am surprised (NOT) by the number of "men" on this forum :)
You wear undershirt with white dress shirts so you don't look like you are smuggling a bear underneath! It used to be the "wife-beater" (sleeveless undershirt, for our foreign friends) and only recently most men started wearing t-shirts, instead. The wife-beater doesn't help in the sweat department, rather just covers the front of your upper torso, which is the part that would be visible with the jacket unbuttoned.
A real man, i.e. one with hair on his chest, would look disgusting with a white dress shirt and no undershirt. And if the shirt is not white - it better be as thick as museum curtains, otherwise it would look like your dress shirt is growing its own hair...