IIRC, Tuesday nights were the nights that Woody and other early BNM/ARC players got together for coop games before the variants community really took off. That isn't too important now except that it's why Tuesday was picked rather than some logical day like Saturday
I don't think V-nights were ever meant to get people to switch from BNM to other variants. (I think the Variants channel might actually predate the Nude Beach one but it has been too long for me to remember the details... I do remember organizing games with Hedgehog(BNM) and Spanky(BAR) in Diablo Retail USA-6 though
It encouraged people like me to play their variants rather than normal characters, and it encouraged people with limited internet access to all choose the same night to play. For a while V-night was a very high priority event... you might see 20 people in the channel on a Tuesday and not be able to get a coop game going on the following Wednesday.
By the way, I'd love to see a D1 V-night return, although no nights are really great for me at the moment