cassettes CAN sound better than vinyl.

The reason cassette recorders were popular was because they could record and store music. 

They were the best available technology at the time. 

Does anyone remember when you could record music on your VHS recorders? 

There are few cassette decks that do a very good job of replicating the source. They cannot beat a good vinyl playback system but can hold their own. Nakamihcis, as good as they are, could not replicate the ambience and image like the vinyl source. The best decks I've heard in my system are Tandberg 3014s. They create better soundstage close to source. 

I agree with Ralph, you lose bass with faster tape speeds. On my RtRs the bass is better at 7.5IPS than it is at 15IPS. The disadvantage of cassettes is the tape width, not enough real estate to put music down and saturate very quickly.

They're fun none the less.

For you tape heads, any takers for my MC Hammer adams family cassingle?  Put your money where your mouth is.

Let’s think of the ways in which a CR-7 could be better than vinyl. Let’s assume that the Nak’s important caps have been bypassed by styrene or teflon, drive mechanism is belt rather than gear, and that the machine is otherwise to spec, and Dolby is not engaged; at least not Dolby C.

If one records a record onto a very good metal tape, say TDK MA (metal frame), or MA-XG (ceramic frame), then the difference between original and casette is small. Certainly less than the difference between a cold and a fully warmed up phono and cartridge.

So, if you carefully warm up your CR-7, your phono, and your cartridge, say 8 hours, 8 hours, 2 hours respectively, then your recordings should be better than a cold phono and cartridge. IMO.

So why don’t I do it? I like variety, and my cartridge may be immortal. And, oh yes, lazy, lazy ...

I used to record all my just-brought albums with a Nak and Maxell/TDK tape. Luckily I worked in an audio/record store at the time so could afford to do that. Although I could not say they sounded better then the LP, it was very close and great for everyday listening. It also kept the records pristine and was especially good when having several friends over having beers and such. Kept the records and even more important, the needle and turntable safe. Well worth it. I still have many of those tapes which are decades old now and they definitely sound better then MP3's even today.