"And we must remember that almost all recordings released after 1980 were on digital files."
This just isn't true, producers were quite actively using analog for recording and mixing right up to the mastering stage before the original analog was mastered to digital for mass CD distribution. It was still felt that recording and mixing in analog was superior until it became financially prohibitive to do so, though many artists and producers still continue to use analog in one form or another to this day.
Another issue that no one has touched on in this thread is that the new tape formulations that were introduced starting in the late 1960s are falling apart. The analog masters still exist in one form or another such as the two track original, flat or equalized transfers or production masters, companies archiving them like Sony who has possession of one of the largest libraries of original masters on the planet won't let them of the premises. They've become increasingly precious since during popular music's hay day the big production companies didn't pay the closest attention to archiving the masters for posterity and many have been lost along the way. Not to mention the massive Universal warehouse fire that occurred in 2008 where tens if not hundreds of thousands of the tapes were lost!
The biggest issue is with the newer tape formulations was when a switch from acetate based magnetic tape to a polyester based one required a new formulation of the adhesive that was needed to glue the magnetic oxide formulations to the tape base. Unfortunately, it wasn't foreseen that in storage the new adhesive was hydrophilic and would absorb moisture from the surrounding air after years of sitting on a shelf. Once the storage container was opened there would be a telltale odor of mildew. Upon spooling one of these tapes on to a playback machine for copying or mastering all of the emulsion would sluff off on to the capstans, pinch rollers, tensioners and tape heads when the machine was started and the valuable music information contained in the oxides would forever be lost!
One mastering engineer kind of serendipitously determined that he could "bake" the mildewed tapes at low temperature in a toaster oven for several hours removing the excess moisture and at least temporarily reharden the adhesive enough so he could get at least get one pass of the tape through the playback machine to make either an analog or digital copy.
If the transfer was considered a success and the resultant degradation that occurred from the improper storage and transferred to the copy during this step and the degradation wasn't too substantial to master in analog, they would painstakingly attempt to restore and remaster it in the digital realm. This is not always the case however since producers and recording engineers had their preferences and would continue to rely on methods that used the older tape stocks that didn't have the storage and preservation issues of the newer ones. It's notable that the early stocks used for recording in the late 1940s through the late 1960s from the likes of 3M and BASF may still be in very good shape today if they weren't completely worn out from constantly being referenced for new copy masters.
There is more to tell on this subject as to why Sony Phillips developed DSD as an archiving format to help deal with these issues and how it was haphazardly marketed to the public as SACD and why Mofi determined they could provide a sonically superior product for their customers working with DSD 256 to make flat transfers on site from these archives and remastering them in house and the public relations issues that resulted from not going public with it early on.
Getting late!