Because of Amendment XVII:

When vacancies happen in the representation of any state in the Senate, the executive authority of such state shall issue writs of election to fill such vacancies: Provided, that the legislature of any state may empower the executive thereof to make temporary appointments until the people fill the vacancies by election as the legislature may direct.

Vacancies are to be filled by special election, but until said election, the governor of the state may, but is not required to by the U.S. Constitution, appoint a temporary Senator if state law says the governor can.   Any vacancies in the House, however, must be filled solely by special elections according to Article I, Section 2 no temporary appointments:

When vacancies happen in the Representation from any state, the executive authority thereof shall issue writs of election to fill such vacancies.

The Senate practice of temporary appointments is, according to the Congressional Research Service, a holdover [PDF] from the original election procedure of senators where, prior to the 17th Amendment, state legislatures would choose the senators for their state:

This practice originated with the constitutional provision that applied prior to the popular election of senators, under which governors were directed to make temporary appointments when state legislatures were in recess. It was intended to ensure continuity in a state’s Senate representation during the lengthy intervals between state legislative sessions.

Another aspect of our government and election system dictated by antiquated rules and practices (like voting on a Tuesday; more on that later), but not if Wisconsin Senator Russ Feingold has his way.   On Sunday, Feingold announced:

The controversies surrounding some of the recent gubernatorial appointments to vacant Senate seats make it painfully clear that such appointments are an anachronism that must end. In 1913, the Seventeenth Amendment to the Constitution gave the citizens of this country the power to finally elect their senators. They should have the same power in the case of unexpected mid term vacancies, so that the Senate is as responsive as possible to the will of the people. I plan to introduce a constitutional amendment this week to require special elections when a Senate seat is vacant, as the Constitution mandates for the House, and as my own state of Wisconsin already requires by statute. As the Chairman of the Constitution Subcommittee, I will hold a hearing on this important topic soon.

Given the recent, shall we say, circus with the vacant Senate seat in Illinois and the odd and ill-fated pseudo-campaign of a certain would-be senator for New York, the power to decide the representative of the people should be left to the people.