Most of Europe and Asia the shop supplies all the specialty tools, if not all the hand tools as well. If a mechanic needs to bring their own kit to work it's typically a very small amount of stuff and would fit in a small rollaway if not a hand box or cart like a Hazet Assistent. American mechanics tend to have to supply ALL their own tools, and this includes some "specialty" tools that are bulky and not space savers at all, hence the bigger boxes in USA.
Once you look at all the stuff required to work on modern vehicles, you can see why toolboxes have grown. Just the electrical systems alone require a few drawers full of testers, meters, scanners, scopes, probes, and all sorts of hand tools. Back in the 60's all you needed were some wrenches, sockets and a few screwdrivers and maybe a hammer or two for general repair. You had "specialty tools" if you had a timing light and a test light. If you did engine work, body work, suspension work or anything larger, you might need a bigger cabinet but still nothing huge.
There is a reason for these boxes and it's not just ego. Although it for sure is in some cases.