Well, you certainly have good points, as always. And you're bring up a different school of thought on the subject.
First, the driver is responsible for checking his/her vehicle every day as part of an automatic daily check. Which is legally required for our CDL vehicles and we opt to follow it for everything else. For the daily check, we do not have a checklist at this time, but perhaps we should. This checklist is designed for our weekly check every Monday morning.
If there is a discrepancy found on the vehicle, one of our three designated shop personnel is alerted to the problem. Either from someone saying, "Hey can you look at this stuff dumping all over the ground?" to a comment on the form that you think we should change the tires soon.
Every Monday, we have a meeting at about 9am after these checks are completed and someone is going through them before/during the meeting to see what needs to be addressed before someone leaves (brake lights are out), can be taken care of during the week (load cover is tearing), or can be repaired during the winter (toolbox door is rusting away).
As far as checking for leaks, you're looking under the truck for puddles and along hoses and lines for dirt that may be clinging to the fluid from a leak. For lug nuts, you're looking for obvious problems like loose nuts or missing studs to prevent
this from happening. We do have two part time mechanics who do a lot, but it's easier when the person who uses the truck all the time notices something's wrong and has a way to report it.
The rest I'll save for a new thread.