Must be tradition because there seems to be straightforward alternative: Northbound! Starting in the first half of June maximizes daylight around summer solstice for the ride. There is a lot of appeal to a group start (increased motivation compared to beating split times) and to having long daylight, but I would (and did) start northbound in early June. Better chance at weather (forest fire season is going to deteriorate for another month in the south, while the north on average will be drier and warmer when you get there).
When McCoy scouted the route and proposed going south, he considered it a 2 months trip which works better going south as described in the book. Don't need to follow that tradition for racing.
Strange that there are comments that the weather is unpredictable - it seems rather predictable that the far north is going to be wet and cold in early June. Having ridden both ways, the NB disadvantages are likely headwinds just when you are most vulnerable (e.g. Basin, NM desert; even though it should average out over the whole distance), high altitude early on, and overall a harder first week (for me, NM is the hardest state by a big margin - and the first day NB might be the hardest of the whole trip).
I had actually looked at the pluses and minuses of each direction last year. This is a summary:SoBo
Pro: More fun to start with more people (but by day 2, that feeling is gone!)
Pro: The maps and cue sheets are sobo. Much easier to follow.
Pro: Easier to get to Banff than to Antelope Wells
Con: Likelihood of more snow up north
Con: Likelihood of crappier weather in the north (includes snow and rain)
Con: Hotter in the south
Con: Might be difficult to find a motel in the first few days if you arrive past 8pm (and this is grizz country, so many people will want one)
Con: tough to get out of Antelope Wells when you're done
Con: colder weather in the north, hotter in the south
Con: difficult to ship your bike via UPS because of the uncertainty at customs (unless you live in Canada.) You need to travel with it which is more expensiveNoBo
Pro: You can ship your bike to some town close by via UPS (no possible delay due to customs, unless you don't live in the US)
Pro: Far fewer people to compete with for motel rooms in the first few days (if you even have to use motels in the South)
Pro: Easier to get out of Banff at the end than out of Antelope Wells. Also a nicer place to stay for a few days at the end, than AW.
Pro: Maybe a little cooler weather in the south at the start, and warmer in the north
Pro: Likely less snow on the ground in the north when you get there
Pro: Less likelihood of real crappy weather in the north when you get there
Pro: slightly cooler in the south than 3 weeks later
Pro: Frontier flies to Tucson, and Frontier doesn't charge for bikes.
Pro: softer official record (assuming last year's record doesn't count, with all the detours)
Con: Harder to get to Antelope Wells for the GD
Con: Harder to read the maps and the cue sheets. More chances for mistakes. There is a SoBo GPS track, though.
Con: if tired, you may not be as on your game as you should be with grizzlies.
Tie: wind! It blows every which way!