You're substantially correct on everything you've mentioned. Bigger cable has lower losses.
Low loss is important in two areas
1) Noise
The attenuation of a feeder is what adds Johnson noise corresponding to its temperature onto the signal. A feeder of near zero length has near zero attenuation and so near zero noise figure.
Up to a meter or several (depending on frequency), the noise figure of a typical cable tends to be dominated by the noise figure of the input amplifier you are using, even cables of pencil diameter (you can get really thin cables, sub-mm even, and in these you do have to worry about meter lengths).
To get signals down off your roof into the lab, any feasible cable will be so lossy, even unusually thick ones, that the solution is almost always an LNA on the roof, straight after the antenna.
That's why do tend not to see really fat cables in labs, they're not needed for short hops, they're not sufficient for long drags.
b) High power handling
In a transmitter station, you tend to have the amplifier in the building, and the antenna 'out there' somewhere. Putting the amplifier 'out there' as well is usually not an option, so here you do have fat cables, as fat as possible given that they have to remain TEM, without moding. That means <3.5mm for 26GHz, <350mm for 260MHz etc.
The impedance of the cable also matters, as well as the size. Have a look at this cable manufacturer's tutorial on why we have different cable impedances, so 75\$\Omega\$ for lowest loss, and 50\$\Omega\$ as a compromise that has settled itself in as a standard.
Best Answer
yes. Even a resistor with no power source will generate Johnson noise. This is thermal noise due to random movement of electrons in the resistor itself.
f in the formula is the bandwidth across which you wish to calculate the noise, it has nothing to do with the signal applied (or not) to the resistor.