SQL Server 2012: How do I eliminate multiple statements in this code to a more efficient, single statement?
This could be simplified. You don't have to create a temporary table to get your unique day count. You can use the COUNT function on the StartDate column directly. 

Try this:

SELECT
    TotalLoadCount / NULLIF(TotalDayCount, 0) AvgLoadCountByDay
FROM
(
SELECT
    COUNT(DISTINCT  CAST(StartDate as date)) TotalDayCount
    ,SUM(LoadCount) TotalLoadCount
FROM
    dbo.Tracker
) x    


Obviously, you can write it directly like this as well:

SELECT
    SUM(LoadCount) / NULLIF(COUNT(DISTINCT  CAST(StartDate AS date)), 0) AvgLoadCountByDay
FROM
    dbo.Tracker


If my understanding of your problem is correct, this query should give you the same result. Let me know if it doesn't. 

I personally prefer the first version with derived table as it helps with the readability of the query. You are not paying any additional cost because SQL Server will generate the same execution plan for both the queries.