It helps immensely in knowing WHY such things are useful, how they can improve (or screw up!) another layer, and where the correct solution should be implemented.

There's an old joke that the difference between computer science and computer engineering is that in the former one assumes infinite speed and infinite storage. Understanding that there are limitations, and why they exist and to what degree, is important.

As already noted, it demystifies the surrounding "magic". There's a confidence and freedom which comes from knowing that nothing in the system is beyond you.

My education indeed went from "sand to Skyrim", from basic physics & chemistry to electrochemistry to discrete electronics to quantum mechanics to semiconductor doping to hand-layout of integrated circuits to automated layout of ICs (writing the automators, that is) to hardware languages (acronym escapes me) to logic to gate theory to basic CPU design to machine language to assembler to compiler design to C/APL/Pascal/Prolog/Lisp/C++ to OS design discrete math to graph theory to raster graphics to 3D graphics, and a bunch of other stuff throughout. It's indespensible because I can look at any problem and grok what's happening all the way down to silicon, able to work with someone writing Windows printer drivers one day and proving a linked crossover bug in the USB driver IC the next while discussing circuit design in between, why an elegant recursive solution causes a "drive full" error under certain conditions, why error handling in a certain protocol is pointless (already handled six layers down the network stack) - to name just a few real cases.

Knowing propagation delay in the gates can explain/reveal the limits of scheduling in the OS. Understanding drive rotation speeds provided the breakthrough of on the fly compression as an OS-level storage acceleration technique.

Take anything away? Just a sensible understanding of how everything works, and ability to drill into detail where and when needed. All learned in about 6 years, and even came out understanding why Aristophanes' plays survived for several millennia (to wit: dirty jokes endure).

What I do day to day (now)? Writing an iPad app for mobile enterprise data. Working under a genius crafting the many layers of abstraction making it fast & flexible, he can (has) describe a new way to represent very high level data, hand me a rough description of a virtual machine to process it efficiently, and I'll instantly see how it runs on server hardware. I can't imagine not having this view. As a part time teacher, I'm trying to get students from zero to binary to writing object oriented games in 12 weeks flat; to do less is to deprive them of the joy and rewards of knowing how things work - at every level.

"A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects."
— Robert Heinlein, Time Enough for Love