"raw baseband signal is digitized and written straight to hard drives" is pretty routine for all US spacecraft these days. The main constraint is how big the hard drives are, and how many are available, which together with the total downlink bandwidth of all spacecraft using that antenna farm limits how long data can be stored in that form. The recording devices at the ground stations are usually full, and constantly writing over the older parts of the buffer, so you have a limited time to get your raw data out and stored elsewhere within your own project. This allows second-guessing and reprocessing of flawed decoding and analysis, but if the digitization itself was wrong, then it's too late to fix, because the output of that is what you wrote to disk.
I remember the last part of the old days of writing to tape, and the giant VCR-like tape devices we used to use for recording and playback. Each of our tapes was nearly the size of an ordinary home VCR! By the time I started working with them, nearly all processing was digital, so we shipped giant boxes of tape around the world, and then assigned the most junior person to sit there for hours on end playing back the tapes and digitizing them locally so everyone else could read digital data from hard drives. The systems I'm familiar with mostly can't do this anymore, because the hardware got too old and we had long since switched to hard drives for everything, but overall that's a big win, since storage and playback of the tapes was a huge hassle.
Different parts of the US space community phased analog tape recording out at different times, but at the moment, if the digitizer was lying to you, you'll probably just have to toss the data and schedule another collection attempt. If you have a weather satellite, it's not a big deal, but I could understand astronomers getting really upset about it. That said, normally speaking, ADC hardware itself is not usually the root cause of the problem; where we make mistakes is mismanaging the metadata, like logging the group delay of the filter in use by a different ADC than the one we meant.