Down the rabbit hole into bizarre 20th century statistics
I agree with you.
Regarding Blup, see here: https://statmodeling.stat.columbia.edu/2012/04/19/demystifying-blup/
Regarding so-called fixed and random effects, see section 6 of this paper: http://stat.columbia.edu/~gelman/research/published/AOS259.pdf (it's also in our multilevel modeling book and in blog form here: https://statmodeling.stat.columbia.edu/2005/01/25/why_i_dont_use/)
I hope this is helpful.
I agree with you.
Regarding Blup, see here: https://statmodeling.stat.columbia.edu/2012/04/19/demystifying-blup/
Regarding so-called fixed and random effects, see section 6 of this paper: http://stat.columbia.edu/~gelman/research/published/AOS259.pdf (it's also in our multilevel modeling book and in blog form here: https://statmodeling.stat.columbia.edu/2005/01/25/why_i_dont_use/)
I hope this is helpful.