My reasoning on why it is not steam bent goes like this:
Green or mostly green wood blanks are made and go into the steam box and are steamed. I assume they are oversize somewhat, with no profiling, or dowel bores. Once well done, they are brought out and forced into forms, then set aside to set up and to dry. And to dry. And to dry some more. Maybe into a kiln. With all this wetting and drying the dang things are no longer 90 degrees, or flat or whatever, just some nicely bent lumps that continue to move - mostly shrink - as they dry out.
Once dry enough to work with, they are then shaped to a good quarter turn and then ends squared and bored, and some profiling.
By the time all that would be done, I would have my 45 degree blanks made, the bed assembled and someone would be sleeping in the thing. Ugly or not.
All of that steam work is well apart from the turnings and boards and other shop work that goes into the bed. That is, the steambending is not used anywhere else in that project. A chair shop that utilizes steam bending - and is good at it - would make many parts that way, not just one or two.
I admit, my weakest skill set is steam bending, having done 'stove top' only, and watched a few videos. Having read about Thonet's trials and tribulations, I respect the craft immensely, but also think it is harder than I know.