The constitution does not require an inauguration in January. The original presidential term expired sometime in March but if there is no president elect at that time, the speaker temporarily takes on the duties of president until one is elected. Probably someone else here remembers more precisely the procedure when a new president is not elected when the old president’s term expires.
What exactly would that accomplish?
“The Constitution does not require an inauguration in January”
The Constitution does not require an inauguration at all. What it DOES require is that the terms of the President and Vice President end on January 20, and that the terms of their successors then begin.
The 20th amendment to the Constitution specifies that the term of each elected President of the United States begins at noon on January 20 of the year following the election