No problem. I'm just a user for quite some time and this question pops up every so often... It's been answered multiple times in the archives, but who reads the archives, anyway... :P
The switching you see in Samsung keyboard is inside ONE app (which happens to provide both script recognition and QWERTY), not switching the IMEs.
Myscript, as far as I know, is focused on providing the users (us ;)) with the best writing experience, they are NOT interested in reinventing the keyboard part again (which they would have to add). They did what they could to let users switch to a different IME using the 'knobs' available from google (effectively Stylus shutting itself down). Switching back would have to be done from this OTHER keyboard one switched to (hence the action bar keyboard button on tablets).
Google without root
allows only invoking the settings dialog for IMEs from a third party app, or shutting down the IME you have now.
With root, one can circuvent the safety measures and 'force' the IME change.
Have a look at https://play.google.com/store/apps/details?id=com.ne0fhykLabs.android.utility.kmLauncher
, or Tasker. Every one of those apps (the ones which switch any of the settings not exposed by Google to be tampered with) requires root.
Quite the same thing for e.g. turning GPS on/off -> notice that appls without root say something like 'GPS not enabled, do you want to turn it on now', and if you press YES you don't enable the GPS. You get redirected to the system dialog where you can turn it on. Again, safety measures -> third party app can't control GPS. It only can launch a 'trusted' control from Google itself.
Quite some settings are locked as such. Rooting allows for going around those limits, but well, requires rooting :>