If you already installed CW for MCU with K60 support, maybe the default install/upgrade settings are set for K60 only.
Have you tried looking deeper in the "install new software..." options and enable the toolchains/tools/libraries for other MCUs ?
Try again with CW for MCU, select menu "Help" then "Install New Software..", select the NXP update site as shown below:

(the image above shows my update status, your dialog will look different, change the checkbox settings in the bottom of the dialog to view other optional installations).
Or maybe it's a problem due to the license for K60 not allowing to select other MCUs, have you tried with a separate clean installation of CW for MCU using the "free license" option ?
Besides this, it seems like current DSC MC56F hardware and software tools are in long term maintenance mode.
Toolchain is still the original Metrowerks one, but at least it gets periodic bugfixes and small improvements, CW for MCU is still based on an old Eclipse release, etc. etc.
Hopefully they will add support for it on MCUXpresso, but if they plan to do it it seems it's a very low priority task compared to support for their new ARM cores.
What I can see from outside is that most of NXP new MCU products are ARM based, with PowerPC, DSC, etc. slowly phased out.