Unless things have changed radically, the business of the people is the business of the Senate.
If it truly is an issue that "most" Alaskans don't care about, I expect they won't vote for it. If we don't find out, then your assumptions are only unsubstantiated air. The petition only requests that the people decide what is valuable to "most" Alaskans.
Election of a replacement gives opportunity to all sides to be represented by the person of their choice. The choice of the people is an old-fashioned thought, I know - perhaps an odd thought to those who which to choose for us. It is just a concept that crossed my mind while perusing some old paper - the Constitution.