To discuss the "change of speed" issue.
Let's ignore the other axes and consider just pitch. The "dot" therefore represent the relative bearing in pitch alone to the target.
Assume I make the initial "dot" at low speed, say with a pitch attitude of ten degrees. Assuming the "target" is actually level with respect to me, that means the "dot" is ten degrees below the aircraft horizontal through my eyes.
Now, if I maintain speed and keep the dot on the target, there is pretty much total agreement that I (eventually) hit the target.
What if I speed up, causing my AoA to decrease? Assume I instantaneously go to an AoA of 9 degrees. If I now put the "dot" on the target, I get a pitch attitude of 10 degrees, so I get a gamma (climb) of one degree. I begin to go "high" relative to the target. As I begin to climb above the level of the target, the act of placing the dot on the target actually causes my pitch attitude to reduce (since Im now placing the dot below my horizon). Eventually, I'll climb enough so that the target is one degree below my horizon: now the "dot" technique causes me to be at a pitch attitude of 9 degrees, equal to my AoA. I enter level flight.
Now I continue level, but as Im approaching the target I find that it still is dropping below the dot (as my "look down" angle increases). So, in order to keep the dot on the target, I pitch down - bringing my flightpath down towards the target again. I'm going to end up 'wobbling' my way towards the target as I successively over and undercorrect, and I believe (though Ive not worked out the maths) that the average will be, in this case, an approach path inclined downwards about 1 degree (the difference between my AoA when I placed the dot and my current AoA).
Its not the most efficient tracking/homing system, but it will work. The yaw plane is similar.