Why would West Point cadets be at duty stations like Fort Leonard Wood and Fort Hood?

They go to bases during the summer to eat a better understanding of the Army and how it runs. They are generally paired up with a LT or a CPT who show them the ropes.

CTLT and some other similar training programs that USMA and USACC offer

I remember seeing lots of cadets at Fr Campbell, KY years ago and never really thought much of it. I was a PFC at the time believing I knew way more how the Army works than any cadet.

Today, knowing a lot more than then, it's necessary for the learning process for cadets to visit those bases.

Their learning never stops, hence the new LT Motor Officer or Supply Officer. They get put into those positions to learn the ropes, so to speak. It's up to the NCO Corps to teach them what we know about our field of expertise.

Yeah, one day they'll be in command, and if you want a good commander, teach them young and teach them well.