This won't kill Durations. As Duration cards are worded, you get the bonus whether the card is in play or not, e.g. Lighthouse says "at the start of your next turn, +$1", not "at the start of your next turn, +$1 if this is in play." Leaving the card in play is just the way to remember that you get that bonus.
Edit: at least, I think that's how it would work? Hmm.