if you are catering or doing off site events I can understand the toolbox/monster roll. But for a regular gig that sure seems like a pain in the rear.
the first few days of a new job I will bring my regular, no name, fold over zippered job loaded with what I think I will need. as the days go, I keep pulling things out to the point of where 95% of the time end up using just 3 blades (the main tool, as big a gyuto as I can get away with, 300 down to 210ish at which point it becomes a chukabocho. A 180-150 petty for silver skin and fish and third, a razor like utility/parer. This group now gets wrapped up in an old jeans leg cut off. looks a bit hokey, but makes life simple.
As for tools, steels etc, most kitchens have something usable. As for my wet stones? Never do they leave my house.