Hand on heart, I can say that out of the above list, even when I had a company car, I checked:
Tyre tred
Engine Oil
Coolant
Lights
....... Ok, I'm running out of items on the list
Ok, I embellished, it wasn't weekly - it was monthly
Oh, and as my last 2 cars have been mine and full of electronics, the Oil, Lights and Coolant are left to the computers and tyres are occasionally checked as WTF can happen to 6mm of tred in 1 week?