You are smuggling your conclusion in with slight technical choices of switchy vs sticky.
If we make the process markovian, ie the probability of getting heads depends only on if the previous flip was heads, then this disappears.
If we make switchy or sticky strongest after a long sequence of switches, this disappears.
You need to justify why switchy/sticky processes should use these switchy/sticky probabilities.
You are smuggling your conclusion in with slight technical choices of switchy vs sticky.
If we make the process markovian, ie the probability of getting heads depends only on if the previous flip was heads, then this disappears.
If we make switchy or sticky strongest after a long sequence of switches, this disappears.
You need to justify why switchy/sticky processes should use these switchy/sticky probabilities.