But you're not getting the benefit of it, since you're getting rid of the extra drawn cards, negating the benefit of a faster draw.
I think I may have worded the card a little oddly. While Trailblaze is in play you draw 1 extra card aside from your usual draw. Afterwards, the card in your deck that follows the extra draw is immediately destroyed (discarded).
e.g.
1 Trailblaze is in play. There are 15 cards left in your deck and it is now your turn.
It is the start of your turn so you draw 1 card, like usual. (14 cards left)
Trailblaze comes into play, you draw an extra card. (13 cards left)
Trailblaze's negative effect occurs, the next card of your deck is destroyed (12 cards left)
You are now free to play cards from your hand.
Hopefully this clears things up. I'll see what I can do to improve wording.