Is there any measure of how much of that reaches pupils and improves their education versus the amount sucked up by middle layers, consultants, prestige buildings, etc?

It might be similar to the US health spend .. high per capita spend, low outcomes per citizens (compared to, say, Australia) .. with a rich middle layer of providers, insurers, etc.

My HS spent millions on a completely new athletics complex. our math and reading scores were in the dirt, classrooms had 70s era carpet growing crap I don't want think about, the band had 30 year old uniforms...but we had a gorgeous basketball complex.