"Typical statistics work is to use a known good model and estimate its parameters. [...] For statistics, the parameters are your bread and butter" Ever heard of non-parametric statistics?
"For machine learning, they are the afterthought to be automated away with lots of GPU power." You seem to reduce statistics to undergraduate statistics and machine learning to Deep Learning.
"A well-designed ML model can have competitive performance with randomly initialized parameters, because the structure is far more important than the parameters. In statistics, random parameters are usually worthless." This is blatantly false see Frankle & Carbin, 2019 on the lottery ticket hypothesis.
"For machine learning, they are the afterthought to be automated away with lots of GPU power." You seem to reduce statistics to undergraduate statistics and machine learning to Deep Learning.
"A well-designed ML model can have competitive performance with randomly initialized parameters, because the structure is far more important than the parameters. In statistics, random parameters are usually worthless." This is blatantly false see Frankle & Carbin, 2019 on the lottery ticket hypothesis.