- would you renounce a permanent heaven?
I'm just intrigued, not calling it a cornerstone of Buddhism. I'm not well versed enough in Buddhism, to say.
As currently phrased that seems to me like a "polling question", of a sort that's against the site's policy -- see "polling questions" in the Moderation policies for Questions -- theoretically the answers to that question could be just endless users replying "yes" and/or "no", which wouldn't be very informative.
Also there's something missing in the question as phrased: "would" is a subjunctive which implies an "if", so: "Would you, if ..." -- if what? If it were possible? If it were offered? If you could earn it?
It may be like asking "would you like world peace?", "would you like to be happy?", "would you like to live in deathless world?" ... maybe too theoretical, speculative, not a useful or practical question.
I suppose you might ask instead, "Why don't Buddhists believe in a permanent heaven?", or "Do Buddhists believe in a permanent heaven?", or something like that.