[Eagle Six]

In your top illustration they left out the V-Twin cruiser type bikes, that by design many will start dragging metal parts in around that 35* lean angle.

 

[Eagle Six]

For most of the non-athletic types they will get nervous in around 20 degrees of body lean (mostly in the head) because they feel there is no support to prevent them from falling over. They don't want to fall over at speed as they feel the fear of crashing. If they bend their neck away from the turn as their body leans greater that 20* yet their eyes see the horizon at less than 20* they can easily become comfortable out to somewhere in around 30-35*. Any more than that and they need time to get accustom to the lean angle while learning to trust the geometry that provides for a stable bike. For the more athletic types that are already used to manipulating body position beyond normal walking and climbing angles and quickly endorse greater lean angles. These are also the type whom normally seek the trill of speed and embrace the lean as a way to sustain it in a turn.

 

[Eagle Six]

It helps new street riders (and some old street rider alike) if they understand that we turn a bike by leaning. Counter steering is an easy method that takes little effort to attain the lean required for any given turn radius and then the counter steering is neutralized and the front wheel tracks normally through the turn until we want to straighten out by reducing the lean/turn and then counter steering in the opposite direction is used again to upright the bike. Counter weighing with our body position can assist in leaning and used effectively by racers and once a rider gets a feel for when and how much weight and how quickly to load the inside peg and outside thigh counter steering takes even less effort, but nonetheless required to get the proper lean angle. We push forward on the inside bar to initiate the lean, when we reach the required lean for the radius of the turn we neutralize the push and allow the front wheel to track through the turn. Then we push forward on the outside bar to reduce the lean and upright the bike until going straight and then neutralize the bar pressure. Counter steering is easy and effective regardless of the size rider or bike. Counter weighting assist counter steering and the larger the rider and smaller the bike the more effective it is.

 

[Eagle Six]

Then, the rider IMAGINES , or VISUALIZES,

Well....that's one way to explain it. Or, simply, to turn left push the left bar forward, the bike leans left and turns left. To turn right push on the right bar forward, the bike leans right and turns right. Or, "push left turn left, push right turn right". Some folks will never understand the principle and will never care to, they just want to know what to do to get the results. A lot more folks appreciate a simple physics explanation then quickly forget and just keep the actions they need to do what they want. A very few need to know all the geometry and physics and fortunately for them there is a ton (maybe 2 tons) of information on the web written by accredited scholars with years of research and fancy diplomas who, will explain it in very complex and never ending numbers and angles. I know I have been down that rabbit hole a few times!!

Just a suggestion, you may want to avoid the "fall into that hole", part. Bikes like to turn, bikes like to go straight, bikes don't like to 'fall' and go crashy-smashy. Riders like falling and crashing even less than bikes do. The thought of falling into a hole while riding is scary to me!