I have seen some of his early work though the book you refer to does not ring a bell.
Many great photographers were able to do magnificent work with basic equipment but in almost all cases they improved their equipment when the opportunity arose.
I admit to getting some very nice images out of my old Agfa Jsolette when things work right. It is also very portable and fits easily in my pocket. The obvious advantage to working with one camera like this is that you can get pretty good at making them work for you.
Of course, for its day, the Jsolette with its 85mm Solinar lens and Compur Rapid shutter was no Brownie, and cost quite a bit more than a basic camera would have gone for in those days.
Interestingly I do own an old Zeiss Icarette folding camera with the equipment to use 6.5x9 cm glass plates. This would have been a later iteration of the ICA that Mr. Kertesz would have used in the early days. The lens is pretty low contrast but everything seems to work ok when I use 120 roll film. There is a light leak in the bellows but if I cover it with a dark cloth it isn't a big problem. One of these days I'll have to coat some glass plates and try it out.