Few riders or drivers actually understand what a late apex is (or even that it matters what trajectory you take through a turn), and most people don't take early apexes because they try to get a "race line", but because they see the turn and their little hamster brain tells them "watch out! the road is ending! you will go off road/ in oncoming traffic! better turn now and avoid the danger".
Apart from the risk of getting the kiss of death from a bus (as shown in Gary's picture), there's also the risk of going too wide and running off the road or into oncoming traffic- more so with turns that have a tightening radius and/or roads with high camber/crown. Even if one doesn't run off the road, the outside part of the road is the part most covered in debris (risk of loss of traction and risk of punctures) so it's best to avoid it, more so while leaned. Another safety bonus of turning late apex is minimizing the time the bike spends leaned.
A good rule of thumb for street corners: start on the outside, get through the middle, end on the inside. If you exit the corner and find yourself on the outside you've just messed up- either the wrong line (turned too early), too fast, or both.
+1 for those books, I'd also add Motorcycle Roadcraft: The Police Rider's Handbook.
