You’re certain of this? There may be a wealth of more music that you just don’t know about! The reels are always marked - they come that way.
My dad had one he bought in 1959. He used it to record reports off the radio when Kennedy was shot and he also recorded some auld fellows in his locale singing and playing homemade fiddles. This was in Northern Ireland.
The radio station where I work was still using open reel tape machines as late as 2003. There were two Otari machines in each production studio and control room. Now there are three machines in the whole building, and only three of us old farts who know how to use them. “What’s that razor blade for?” “Editing.” “Huh?”
We have to keep some machines to be able to play thousands of tapes in the news and programs archive, going back to the '50s. They will have to be transferred to digital before they deteriorate to the point of unplayability. Tapes made in the '50s and '60s are still holding up well, due to the fact that they were made using whale oil. But in the early-mid '70s, tape manufacturers started using synthetic oil in the process, and now that oil is decomposing. Already, thousands of tapes all over the world are turning into a gooey, sticky mess, and everything on them is lost forever. This includes the master tapes of some of the world’s most popular music recordings.
I have an early '70s Sony quarter-track mono machine at home. I get the occasional request to transfer someone’s tapes routed to me from other facilities in town, because nobody has any equipment to play them on. Professional machines run 7 1/2 and 15 IPS, and are usually either full-track mono or half-track stereo. Home machines run at 1 7/8, 3 3/4 and 7 1/2 IPS and are usually quarter-track stereo or mono. I used to have a Phillips stereo machine, but the motor burned out and I couldn’t find anywhere to get it fixed, nor the parts to accomplish it!
To answer the question about cart machines, they have been obsolete for a long time. Some ill-equipped, low-budget stations are still using them. But they were replaced by Minidisc decks in the '90s, which did everything anyone wished a cart machine would, only better. Those in turn have been replaced by the playing of .wav files from a computer.
Any of you radio types remember the Ampex AG-440? It was the Lamborghini of tape machines. How about Crown (the amplifier people - they made tape decks once, too)? They were more like the Cadillac of tape machines. Not too great for heavy use at radio stations, but really nice. I never met anyone who owned one, but saw them in stereo shops.
Although I never purchased any professionally recorded media on reel-to-reel, I still have my portable Realistic 5" unit and a Philco 7" unit.
I have a bunch of tapes stashed away that I intend to listen to and go through and convert anything interesting over to digital files so I can file and listen to them easier. They have been stored in a dry, cool, dark closet, so I think they are still in good shape. I believe the thicker tapes were mylar and the longer, thinner tapes were polyester.
There is no telling just what I might have scattered around on those tapes. There should be some radio recordings from 1967-1969, when you had to wait until midnight when the single FM rock station would play “underground” rock music you couldn’t hear anywhere else.
There should also be some TV theme songs and episodes from that time, as well as class notes from high school science and speech classes, maybe even some recording from band class. I will just have to listen to them all to see what interesting things might still be on them and mark them for digital conversion.
I was just going to say repair was one of the advantages of reel to reel. If a cassette tape breaks, you are basically SOL - I’ve never been able to fix them. Back then you could buy a splicing kit - basically a little platform with a diagonal groove, a razor blade, and some thin scotch tape, and repair breaks. Much better to lose a fraction of a second of a tape rather than the whole thing.
I’ve fixed plenty of cassettes with just such a gadget, but then you do have to have one of the cassettes that are screwed together.
Radio Shack used to sell (and may still sell) cassette repair kits that included a new shell. Even so, cassettes were still a lot harder to repair than open reels. Eight tracks were even worse.
You can have sensitivity and selectivity, it just costs money. Most audio equipment is primarily designed to be cheap, not for top performance. Considering how the average FM station butchers its audio, it probably isn’t worth it to design a really good receiver.
Yep, I forgot the eternal Truth: You can have it good, fast, or cheap - pick a maximum of two. 
Fundamentally, I still say you have a tradeoff - it’s just that with enough money you can increase each enough that it doesn’t matter.
At my middle school in the late 1980’s, my French teacher still used reel-to-reel tapes that lessons were recorded on. Considering how hard it is to understand a foreign language even when spoken clearly, it was often a real pain in the buttocks trying to deal with the crackles and muffled voices on these tapes.
Back in the sixties, after watching black and white TV for years, we finally got a color TV, just in time for the premiere of Star Trek. At the same time, my mother got us a 3 inch reel to reel tape recorder. I “inherited” the B&W and it had a headphone jack. I sound discovered you could plug the TV into the recorder and recorder all my favorite TV shows. Sadly, today I only have a couple of hours left that I transfered to two cassettes. Parts of “Wolf 359”, “The Trouble with Tribbles”, 1968 and 69 Grammies, “The Baron”…