To discuss the topic further, and if one wants to remove the general purpose process from the scope (and not only the screen and the knobs), if I'm not misunderstanding you, the problem in your opinion would be porting the software from the scope to the computer.
That is, you are arguing that transferring signal analysis, deconding, etc etc, to the computer would be too much effort. That is, porting from ARM to x86 (here I'm supposing that the scope has a general purpose arm processor like the one you find in your phone). Now I'm not an expert of that but I think that the difficulties in writing DSP software for scopes lies in the algorithms. Porting these algos to another arch would be just a matter of patience, UNLESS they have been written super low level in some kind of assembly language, which I doubt.