Should the use of K.K. be restricted?

KK is based on the IPA but changes some of the symbols.
See here;
ccms.ntu.edu.tw/~karchung/intro%20page8.htm
for details.
If I remember rightly, it arguably simplifies too much by combining two phonemes into one symbol; I can’t remember the example. It may be /o/ and /oh/ as mentioned here;
ccms.ntu.edu.tw/~karchung/intro%20page%2025.htm

There are not actually that many differences between the British phonemic alphabet (I presume that’s what you mean; the one with the 44 symbols, right?) and the American ones (I seem to remember there are two major versions commonly in use).

It is used for teaching EFL to adults in the UK. As such I think it can be a useful tool if used carefully.