I think it is feasible to use an analogue RF front end under computer
control, the a PC controlling the VCO and sampling the logarithmic
output.
In essence just replacing the oscilloscope as the display system.

I guess, it is not necessary to PC control the VCO. Sweep generators
are easy to come by. probably, if there is a way to feed the sweep
into the PC to generate the X-axis, then that might be a better
alternative.

Having the PC control the VCO via a digital-to-analogue converter gives the
PC a lot of control over the sweep rate etc. You could then control the
sweep rate, and zoom in on areas of your choice, via the PC rather than
analogue controls. But either way would work fine. You can feed the sweep
into the PC with a simple analogue-to-digital converter no problem.

Hans