It seems like because of the huge number of counts that are being displayed. This requires the server to fetch the count independently.
This isn't the case in your inner posts. From your statistics (Google analytics or similar), do you know which part of your site gets the maximum hits?
Top 10 echo count wasn't designed for homepages with a lot of posts that display the count because you can either have a cached number when you use a caching plugin (to reduce lookups) or a relatively slower page (to display the latest count).
What I mean is, that there is one workaround of not calling the count.php file but just using PHP inline. Since you are using W3 Total Cache, you're homepage won't display the latest count.