cassettes CAN sound better than vinyl.

Um...no.  (Former owner of Nakamichi 1000 and avid live recorder back in the day.)

The only reason I had a Dragon was to record cassettes for the car, nothing else. I was in the business at the time and got a swell deal on it.

As others have said, live mic to 2-track (or Tri-Mic) on a clean, well aligned, degaussed crystalloy or sendust Nak or JVC or Sony portable recorder certainly made for some enjoyable listening back in the day, and I have fond memories, but how can a knock-off from an LP beat the original, even on RtoR?  And never mind finding compatible playback on random decks without carefully matching head alignment. The Cassette Era SUCKED!  Good MP3 is waaay better if only because of its immunity from playback compatibility, pumping and breathing, dirt, stray fields, etc. Both formats are lossy, but in analog it’s a mess. 

stager

The best cassette decks like the Nakamichi Dragon or any of several other high performance Naks (I have a 682ZX) or Tandberg or 3 head Tascams, using Dolby B, are capable of recording a signal with wider frequency bandwidth and less noise than mastering machines like the Scully and Ampex decks which were used for some of the most treasured recordings ever made.

That's simply not possible. The wider tape width and higher speed of reel-to-reel give it an inherent advantage over cassette. There's really no comparison. For example, that's why tape deck manufacturers used -20dB levels when they quoted frequency response for cassette decks. You really don't want to know what it looks like at 0 dB.

Aiwa made some incredible cassette decks at the same time those Naks were made, mainly the top of the line f990. I had one, but sold it...as I owned three Awia decks. I still have both the f770 and f660. You would be hard pressed to distinguish between the source material and the tape. Awesome machines. I generally use TDK and Maxell tape type 11. Some pre recorded tapes sound absolutely wonderful on these machines.