White spirit is itself somewhat oily, so whilst it shifts grease it doens't clean to the required cleanliness for brakes.
Brake cleaner has never worked for me. Supposedly it contains something for anti-rusting, maybe it's ok for cars but it seems awful on my bikes - even the Muc Off bike specific one.
Clutch cleaner works brilliantly, but it doens't last long.
Acetone aka nail polish remover is effective but damages some plastics, I'd be wary
Meths is good ime
Rubbing alcohol seems not to be widely available here, surgical spirit is though and that's just methanol and ethanol I think, works well on brakes.
Electronic contact cleaner also works very well indeed, I think it's the same as clutch cleaner though - smells like it.
Soap and water works rather well too, if you agitate it. Also water on its own is quite good, for lightly dirty rotors. On the trails I find a puddle with some fine mud in it and rub it all over the rotors with finger and thumb until it gets squeaky. Works a treat.
DO NOT use a sweetened drink from your camelbak though - the sugar or whatever is in there goes sticky and the brakes will squeal like bastards for ages.
Why would anyone need to clean their rotors?
I don't know, but my brakes often benefit from it. I have no idea how they are being contaminated - maybe I have a micro leak in the hose or seal and traces of brake fluid are getting on there.