Other negative is price. If you are going to change your oil every 1200 miles or so, full synthetic is really not necessary. There will be just as much contamination at oil change regardless of type of oil used (oil makes no difference in this regard). All modern oils will do a fine job of lubricating a motor, especially one that will likely never even see 20,000 miles. The real difference is how long before the oil starts to break down, and it is unlikely any modern oil will start to break down by the 1200 mile mark.
An option is to have the used conventional or conventional/synthetic blend tested at 1200 miles to see if there is actually an issue (something that would justify full synthetic), then you will know for sure if the added price is worth it.
Again, it is personal preference, and if someone just wants to run synthetic, great.