I use the tonneau 95% of the time, even leaving the car over night, outside. The exceptions, where I will use the shower cap over the top. (Due to the paddling pool effect ably demonstrated in Marcus’s photo, I’d never use the shower cap without either the tonneau or full roof on, underneath) are; car parked outside and either heavy rain predicted, or heavy winds and anything above light/moderate rain. Or, occasions when the car is parked for a long period, overnight etc on the street or particularly public place. In which case I’ll put the shower cap on, regardless of weather, as it helps keep prying eyes out the car. - and you’d be surprised how effective that generally is.
The tonneau cover also gets used when driving solo, it keeps a lot of the turbulence out of the passenger side of the car, and makes a big difference. Works just as well like this with aeroscreen or windscreen, side screens or wind deflectors.
And lastly, parked up in the sort of hot weather we’ve had recently, with intense sun shining down on the car, I’ll flip the drivers side of the tonneau back on, even if I don’t do up all the poppers. It keeps the sun off the drivers seat, and avoids melting the back of your legs etc when you climb back in!