I think there was some technical bandwidth limitations hit with the reproduction capacity of audio tape systems and telephony that made it impractical to continue with Kansas City Standard modulation schemes. It probably can be demonstrated to work at higher rates with cherry picked equipment, but in the main different multi tone encodings were used, and things like quadrature amplitude modulation replaced it. i.e. you can go faster but it's a contrived situation, or you can go faster but we're not in Kansas any more.

For the uninitiated the classic version of the Kansas City Standard was 300bps, whereas the American Standard is 3.8 litres per flush 🤣 you're welcome.

I think same, bandwith and line quality is a limiting factor.
While I can't say much about datasette and BBS times, I do remember Packet Radio on CB radio.
Here, we had used 1200 Baud AFSK due to the limits of the medium (2 to 3 KHz bandwitdh).
There also were users doing 2400 Baud with modified modems, but this was already hitting the wall.
9600 Baud wasn't really possible because no CB radio had an FM discriminator output/FSK input.
There merely was one modem family that had a DSP and claimed to support high data rates via AF connection.
The MHE 4800 (a modem) and MHE 9600 (a TNC), according to my knowledge.

The standard KCS used a number of cycles of 1200 and 2400 Hz. For 300 baud, this is 4 cycles of 1200Hz, and 8 cycles of 2400Hz. Halving the number of cycles doubles the baud rate. By 2400baud we are talking 0.5 cycles of 1200Hz and 1 cycle of 2400Hz. Obviously smaller fractions of cycles will be quite troublesome.

The MSX doubled the frequencies to get its 2400 baud mode to work, so 1 cycle of 2400Hz and 2 cycles of 4800Hz. You could of course double the frequencies again, but now you're running into bandwidth limitations. So, for KCS you're pretty much finished at 2400 baud.

This is where PWM comes into its own. A short cycle and a long cycle indicate a 0 or 1. Half cycles could be used instead, although with less reliability. Certainly you could get 4800 baud to run.

Problem remains the medium, though.
I remember that the Sharp MZ-80K uses 1200 Baud for datasette, but by default the tape routines do also add a lot of copies of the data blocks for error-correction.
Which in turn increases loading times again, reducing usefulness of a high baudrate.
The Sharp MZ-80B (graphics abilities) uses 2400 Baud by conrast, though.

Anyhow, the musical cassette is a very poor medium.
It suffers from flutter, wow and warble. Among other things (DC noise, hiss etc).
Way back in the 1970s radio amateurs doing 8 second SSTV had used musical cassettes (MCs) and noticed how unreliable they are in comparison to real reel tape machines.