We're all working with systems that are partially automated, and the reason there's a human pilot is that the system is not fully automated, or the automation is not fully trusted. So, when you're using an automated system today (or creating one), you still have to do a lot of things manually, and half of them make you go "they/we should have automated this one! it's a no-brainer"
It's indeed weird that a more sophisticated system is not automated in this regard, but even our less sophisticated systems are often requiring our input for things much sillier.
So:
1. Maybe the system didn't give the green light - the ship didn't fly, after all.
2. Maybe it should have been dead obvious to the pilot, like closing the front door during winter.
3. Maybe nobody bothered, because rarely anyone forgot.
4. Many episodes and films plots rested on creative use of the ship systems. Going to warp with the external inertial dampeners on might have some weird use. If the system forbade you from doing it, your options will be limited by one. Starfleet probably discovered early on that their systems should be flexible, giving the pilot the ability to do unorthodox things, and the Enterprise allowed Sulu to do this, assuming he was doing one of those things.
5. The ship was just constructed. Perhaps it wasn't yet tested enough, and the warning light for this malfunctioned. Showing glitches, just like its crew straight out of the academy.