I'm lucky enough to have a dedicated space in my basement for a small desk & shelving for material storage. The only thing stored IN my desk are my tools in a large flat Plano Box and hooks in Umpqua hook boxes.
Pre-threaded bobbins are stored in a plastic box on shelves in front & beside me along with the rest of my materials in plastic boxes, Rubbermaid containers, etc. All body/wing materials excluding hackle are stored by color (browns, black/greys, cream/yellow/red orange, olive) in separate bins and other misc. stuff like wire & other ribbing are in separate bins.
First off, when I tie the ONLY thing on my desktop excluding head cement, dubbing wax, etc. (in a small plastic box) are the tools & materials for the fly pattern I am tying. When I change patterns, I put away the stuff I don't need and take out the stuff I do...
When travel, I decide in advance what flies I plan to tie and in a cheapo Bass Pro Shops duffel bag I put in my travel vise & light along with a few pre-loaded bobbins, the Plano box with the other tools, the head cement "box" from my desktop and only the materials & hooks I need for the flies I plan to tie which are already in separate containers.
This system works for me and other than having a specific travel vise & light, I don't need a separate (expensive) travel bag I have to stock or check before a trip.
When traveling if I feel a need to "match a hatch" and don't have what I need, I improvise or deal without...