It's all ready setup with population, both high and low, taken into account. This is what sets up the timing of the opening and closing of the arenas.
When the numbers in the split arenas become too low and create issues with playability they close the split arenas and open the off hours arena. This "time" that they have picked to do it is for two reasons. 1) it's the general time of day EVERYDAY that the population drops to these numbers (HTC has the numbers so I'm sure they have it pin pointed pretty well) and 2) they give a "set time" so that the players can set up there "last minute base grab" missions
No it so that the people will get trained to know "when" the switch will happen, and plan accordingly.
The change from off hours to split is thought out the same way. As the number approach that magic number that makes the arena become unhealthy they switch it back to the split arenas. The timing again is set due to at least two factors. 1) Like the change to off hours, it's to give the players a time that they can plan their missions around. Being the same time each makes it easyer to get us to. and 2) the timing of the switch is again tied to the population numbers. It is set to when the numbers from the US are loggin in with big enough numbers to bring the population number in BOTH arenas up as quick as possible. Do the switch earlier and it takes FOREVER to build numbers in the arenas to make it fun. Do it later and you run into that unhealthy arena problem again. Again, I'm sure this is based off of HTC numbers that they have available, but we don't.
Having the arenas open and close as the number move up and down all day would be more frustrating than it is now. Closing out an arena because the number fell a bit too much would piss the people off that were having fun in that arena, and opening a 2nd arena when the numbers climbed a bit would suck because you couldn't count on the numbers climbing quick enough to make it fun for those going into the second arena.