cassettes CAN sound better than vinyl.

When I had my shop, we used to put a record on and a tape we recorded on a Nak and switch back an forth on an Audio Research/Magneplaner system.

The ONLY difference we heard was a "hollow" sound (best word I can use to describe it--same word we used in 1976)--on the tape deck. Otherwise, the Nak and the vinyl sounded the same.

FYI, back then the vinyl was played on a Linn-Sondek, I think, with either a Supex or Satin cartridge, but it has been a while, so...might have been a Thorens and Decca, but Thornes were very inexpensive back then, so we might have tried both. We used SME arms, I believe...

Biggest issue back then was that every Nak deck broke pretty quickly and had to be sent back for service. They did it, but customers were not pleased!

Cheers!

Given how many of the excellent bootleg live recordings from the 1970s were made on cassette decks (Mike Millard, Dan Lampinski, JEMS, etc etc) clearly quality can be had (most of these gentlemen went to Nakamichi decks with good quality microphones) in that mode. 

So compared to the average Joe whose turntable might not be audiophile grade, records themselves worn and poppity etc, the OPs statement is correct, can being the operative word.

I recently purchased and enjoy the music from a Nakamichi 
Cr3a deck. Highly recommend 
Pam, the Nakamichi salesman from California.  He has a technician who specializes in
refurbishing Nakamichi cassette decks. I’m totally impressed with
its ability to play music. But better 
than vinyl? 

My NAK BX300 sounded astonishingly good with clean and adjusted heads...it's now been mothballed and could use a tweak/cleanup and belts I imagine...also, no space in my gear heap rack...CD player, streaming devices, preamp, amp, power conditioner, laundry conditioner, a tiny nuclear power plant, maps of Cuba...