I actually don't think Axl is crazy at all, at least not anymore. His stage lateness is calculated, it's certainly not because of drink, drugs or general unreliability, by most accounts these days he is a focused, consumate professional.
He comes on late because he knows no GnR fan is going to go home early, all will have accounted for his unpredictability at concerts, and bad moods at GnR concerts have a habit of exploding into intense nights when he finally takes the stage. When he does take the stage, well, his voice may have diminished over the years but he is still highly practised musically, and has put a ton of effort into the stage show.
Whereas bad moods at STP gigs just result in everybody going home pissed off.