I think Satoshi wanted to use the 2016 number as an Easter egg to the US 6102 executive order. Also, it’s enough time to get an accurate average of block times. Daily would probably be much more volatile as a few quick or slow blocks could throw the average time way off.
Discussion
I think even a week worth of blocks would have been enough duration to get a decent average, and keep the adjustment from being thrown off by a few longer block times, or really short ones, but a day definitely would be too short a time. So, the need for a smoothed out average explains why the adjustment doesn't happen daily, and the fact that 2016 is 6102 backwards explains why it was set at every 2016 blocks specifically.