>why does American tech organise itself this way, a completely different way to other professions?

The massive shortage of software engineer talent over many decades has created a situation where any work that a SWE doesn't like to do is carved out into its own role so that the SWE's job description stays fun and attractive.

DE, DS, BI, SDET, SRE, QA, FDE, SE and to some extent even PM are all roles that emerged from the boring stuff that SWEs don't like doing.

>Do SWEs value the input of their EM? Does it really add value, or a bunch of busy work?

Depends on the EM. Usually though, no. Usually EMs earn the respect of their reports by doing the people side of things really well, not by having extraordinary technical inputs.