I was quite happy to see that FeedBurner had integrated site visitor tracking in addition to their already great feed usage statistics. Actually using it with my blog was just a matter of cutting and pasting some code into my template. Here's the snippet that I was offered for Movable Type:
That would have meant that the same tracking code can be used across all sites thus most users would have it cached (I think that's what Google Analytics relies on). Unfortunately, that's not something that I can change on my own.
However, when running into a related problem (a FeedFlare was stuck on) it was pointed out to me that the
i=... part of the script URL can be removed if all that's desired is the visitor tracking and not per-entry features like FeedFlares. This means that at least across my entire site there is only one tracking script URL that visitors have to load. It turns out FeedBurner documents this, but only in the "Others..." category (the bottom "If you want to use StandardStats only" section).