Is there a reason why type 3 tapes didn’t catch on?

I don't even know what Type 3 tape is.

I don't care what it is.

Type III Ferrichrome tape

https://en.m.wikipedia.org/wiki/Compact_Cassette_tape_types_and_formulations

Cassette tapes are more about convenience than they are about sound quality. One might say that the CD made the cassette obsolete. 

I was in the audio business back then. They were very expensive compared to everything else and then Metal tapes came out soon after, which if you were going for the best sound for cassettes and pay good money for them, you'd just go for the metal ones. People either wanted cheap (to make a 10th generation Dead or Bruce tape) or the best quality to tape a record and listen to the tape for convenience. 

I used the TDK SA-90s and Maxell XL-IIs and certainly cost impacted what tapes I purchased.

Incidentally, the tapes I created are still functional.  However, if you consider the source of a quality tape deck in the 80s against another source like a Rega P1 or Node 2i...the tape doesn't fair very well. 

Yes, Metal tapes killed it.  I stopped using metal (cost) after getting AIWA deck with Dolby HX-Pro (servo on bias).  It provided great extension even with less expensive tapes.