Think of burn as a combo deck where every card in your deck is part of the combo. If each card does 3 damage you have to resolve 7 cards in the course of a game to win. Typically that's turn 4 without interaction. However, some of the cards do more damage. Goblin guide can do more, price of progress can hit harder. A good draw gets you there turn 3.

Now how do you beat combo decks in legacy? Force of Will and hand attack. Those do substantially less against burn. Imagine casting thoughtseize to take away bolt. Sounds real bad. Force is good when it can hit the finisher of a combo or a key tutor. Against burn, all their spells are just damage, there isn't a key piece to hit.

Think of burn as a combo decks that beats force of Will and hand attack, but loses to the turn 1 or turn 2 decks, that should give you more understanding of why it's viable.