"Looks like the early developers of mixed methods studied how adults actually read and developed their method for teaching children according to that"
Ther thing is, 'directly copying what an expert does' is not necessarily an effective way of learning to do something frtom scratch.
I was thinking about a parallel with ballet [which I know a little about due to DD]. A small child 'copying what a ballerina does' will not be able to become a ballerina via that method.
EITHER that child will have to break each thing the ballerina does into small steps - e.g. to realise that in order to stand on pointe, they will initially have to strengthen their feet through pointing exercises, through raising and lowering onto demi-pointe, through learning to stand on demi-pointe for longer and longer times, and then gradually on to pointe. They will also have to somehow work out the correct way of doing each of these things so as not to distort the feet, to achieve the correct foot and leg alignment etc.
This is essentially what mixed methods of reading do - they ask the child to 'copy an expert' and hope that along the way the child will intuit the correct processes that underlie what the expert does. About 80% will manage that (possibly less with 'pure' L&S, because at least most mixed methods do have an element of phonics teaching)
OR the child can be taught the underlying process of ballet directly, through a series of carefully-graded and standard exercises (all those French names for steps), so a dancer will arrive on pointe having all the underlying processes explicitly taught and secure.
That is more like synthetic phonics - making all the steps explicit and secure through direct teaching of them, even though in the end the end product will look exactly the same as the expert studied at the beginning... (via this method, 95% at least will end up becoming expert).