Why wouldn't you use earth straps when they are supplied with the tray and trunking?? Before they started supplying earth straps, all our metallic containment systems (apart from conduit) in the factories I did my training in had to have a strap between joints etc. Every project i've ever worked on, call for them!! I'll stick to what i know and have done for over 40+ years, ....the straps go in!! lol!!
I can't ever remember using painted Tray Or trunking, it was always Galvanised stuff i've ever used. I take it your referring to the grey trunking, (can't remember try being painted) often used in office buildings etc??...