There were tons of moments where KITT drove himself on the old show. Most of them were really brief, like KITT driving up to meet Michael at an entrance or coming to the rescue (hence the famous "KITT, I need you" line), but they were still cool as hell. I never got tired of that little dashboard startup sequence we saw in nearly every episode.
I forgot, we did see the new KITT driving himself at the start of the premiere, although somehow it wasn't nearly as magical. Not sure if it was the car, or the fact the novelty has just worn off...
I liked that startup sequence too first the dashboard, then various other things like "fuel pressure* and the later seasons like the light up foot peddle and an automatic never looked so good shifting to "D" lol
It's probably fair to point out that since KITT didn't have a standard engine he probably didn't have a stadard transmission either. He probably had something akin to what we today call a "CVT" or continuously variable transmission.