What is the advantage to accessing the truss rod from the bottom of the neck as opposed to the headstock?

My guess...
You don't have to remove the strings to adjust the neck, merely loosen them a bit. The strings have more flexibility at the 24th fret, you can get them out of the way.
 
Mike

I think the main advantage to having the truss rod at the neck/body joint is that you don't compromise an area that is already at risk for damage. I would bet anything that the most common damage to a stringed instrument is a headstock busting off. Without drilling a hole up there, you get to keep more structural integrity. OTOH, it may not make a difference!
 
Edwin