It is generally applied as far as I know. One thing that makes it tricky to implement in some situations is that it may be more vulnerable to certain side channel and fault injection attacks than "straight" RSA. Those attacks may expose the prime factors and thus the private key.
I cannot see other reasons why it wouldn't be implementable on some platforms, except that it may be somewhat more complex. It may use slightly more memory, but on embedded systems, performance is usually a great good as well.
Note that the private key is usually kept on the system doing the RSA CRT operations. The public key is identical. So you may not always see that it is applied from the outside.