Shorter vote counting times can lead to shorter lame duck periods (over time).
Until 1937, inauguration day in the US was in March, about 4 months after the election. This allowed time for votes to be tabulated and reported, which took more time given the technological limitations of the day. One downside to this was the lengthy lame duck period between the election and inauguration, creating the potential for ineffectual or erratic leadership. Over time, as vote counting became speedier (among other things), this lengthy lame duck session became unnecessary, resulting in the 20th amendment, which moved inauguration day to January. In this case, improvements in vote counting times contributed to a real change in how political power is wielded between an election and inauguration.
The upper limit of vote counting times is naturally the lower limit of the lame duck period - you shouldn't schedule an inauguration day any earlier than you're certain to have the final count. If votes could reliably be tabulated on election day itself, it would be possible to move inauguration day to the very next day, eliminating lame duck tenures entirely. I'm not suggesting this would be a worthwhile or desirable endeavor, but reducing lame duck sessions is a reasonable goal of tabulating votes in a timely manner, which extends beyond simple curiosity or anxiety about the result. How much one might want to reduce the lame duck period is another matter for debate (4 months to 2 months seems reasonable to me, 2 months to 1 day perhaps not).
For any scheduled election/inauguration, however, there is no real benefit to tabulating votes immediately or the day before inauguration - so long as the tally is ready in time, it doesn't matter if it's early. For the upcoming election, finalizing the vote count earlier than 10 days post-election would have no immediate benefit.