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In short, I do not understand how or why the migratory aptitude is as listed in every textbook I've read.
Firstly, they talk about a positive charge being built up that is stabilised by the movement of the most substituted group.
I cannot fathom such a build up in my mechanisms.
Please help me understand this in a mechanistic fashion.
The migratory aptitude list for the Baeyer-Villager oxidation is as it is because that is how the molecules undergoing the reaction behave. When we are learning about new reactions from a textbook, we often read about the mechanism and theoretical explanations of chemo-, regio-, and stereoselectivity. It is easy to forget that the experimental observations came first.
The migratory aptitude list $(\ce{H>R3C>R2HC}\approx\ce{Ph(>H)>RCH2>Me})$ is the result of many experiments. Nor is it a linear list as is usually presented. $\ce{H}$ migrates more readily than tertiary groups, which migrate more readily than secondary groups, which migrate more readily than phenyl groups (which migrate more readily than $\ce{H}$).
The mechanism and theoretical explanations came later. The partially complete mechanism from the Wikipedia page is shown below. The key step (center) is a concerted collapse of the tetrahedral intermediate with a [1,2]-sigmatropic shift of $\ce{R}^1$ and ejection of the carboxylate leaving group. Note that this mechanism shows none of the proton transfer steps.
Since the whole thing is supposedly concerted, I can understand your objection to the build-up of $\delta^+$ on $\ce{R}^1$. However, with the exceptions of the anomalous behavior of $\ce{H}$ and $\ce{Ph}$, the migratory aptitude list is the same as the carbocation stability list. Thus, researchers looked for a link between the two phenomena and a way to relate one to the other. The link may not be real, but the trends are there. To a student learning organic chemistry, it is much friendlier at first to apply an existing trend in reactivity to a new reaction (with an exception), than to learn a whole new trend that is unrelated but cosmetically similar.
