I'd like to suggest a menu choice for bags called something like "Examine Contents".
Simply put, Examine Contents would allow you to view the contents of a bag without having to de-quip and re-equip with the target bag. It would be in-force only if
a) it's yours on your floor (prevents visitors from examining so continues to provide a level of privacy, as is now the case)
b) it's no-one's and in the wild.
Maintaining any sense of order gets hard not only if you hoard, but also if you craft in large quantities, made even worse if you don't specialize in only one given skill line.