Does Mana Barbs interact with Mana Web? I would assume that only works if they float mana in response to the tap trigger.
Absolutely right. They have to tap the lands for mana to take the damage, but it makes the thought of, "I'll just tap them all for mana," go away. I've done this before and you'd be surprised how often people tap for mana just in case they need it later in the turn, but I also play a lot of cards like
flusterstorm.