RG6 has less loss than RG59 per length, and is more suitable for satellite dish, but can be used for other things if you don't mind the thickness or price. The reason is that the LNBF output is a higher frequency than your typical signal from the RF modulator or even OTA antenna, and the higher frequency, the higher the loss a cable will make the signal. In other words, higher frequency requires better cables. But if the length is not very long, and if the satellite signal strength is quite strong, RG59 can be used as well.
The LNBF does not output the "13V / 18V". The receiver outputs a 12V or a 18V to the cable, and they are DC voltages. This power serves 2 purposes. One is to power any devices in the line, be they in line amp, switches, and LNBF. The second purpose is to tell the LNBF which antenna pattern it should be receiving in. 12V and 18V corresponding to either Right Hand Circular Polarization or Left Hand Circular Polarization. With 2 independent kind of polarization, a satellite can double its capacity without doubling the frequency bandwidth.
The transponder does not reside on the LNBF, it resides on the satellite in the sky.
Coaxial cables have a set limit on AC or DC voltage limit, but it is silly to say that it doesn't like voltage and will burn out without saying what the unit is. The DC present on the cable is merely 18V and can hardly burn anything unless there is a short.
One must be careful when using the terminology "RF" as some of you have said that "RG59 is only for RF only" and ironically it is not incorrect but I'm sure you meant that it was for TV out. RF stands for Radio Frequency and technically speaking the output from the LNBF is also RF. The difference is in the frequency. RF modulated output is usually set at TV channel 3 or 4, so it is in the lower VHF band and is considered fairly low in frequency. The LNBF outputs at aout 1.2GHz and is considered fairly high in frequency, but it is still RF. Basically a large part of the electromagnetic spectrum is considered RF.
An RF signal is not voltage, or should say it is not merely nor necessary voltage. Technically speaking, RF signal is an electromagnetic wave, and is considered in the form of a electromagnetic field. When the signal is received in a receiver, for example, then it is represented (or should say converted) to electrical signal of a certain pattern (same or representative), in AC voltage. One can argue that an RF signal is represented as an AC voltage in a receiver circuitry, but the signal itself is not voltage. It's like saying that your shadow on the ground is you, which is not true.
If certain receivers work better w/ an RG59, it is not because of them being older, or have better tolerances. It is possible that some receivers have a better receiver sensitivity and thus can pick up the signal better than others when the signal is weak. I have experienced that not all receivers have the same sensitivity (but do not judge it from the signal strength meter, which is artificial and relative).
It is only certain application that AC attenuates more than DC, and it is certainly not true in this and it should not be applied as in the electric power distribution. In this particular application, the more critical element is the AC part, which is the RF signal coming down from the LNBF to the receiver, and thus requires the better RG6 cable to carry. There is a certain loss of the DC power from the receiver to the LNBF etc, but it is usually ok, as there is a high tolerance on the devices using that, and is thus not considered critical. If it is so long that it becomes critical, then the RF signal coming down should be in even worse shape.
There are quality differences among RG6 brands and models and so do RG59 ones. Poor quality cables will have higher loss among other problems, regardless of the type. If the cable is worn or has crack or fold, then the performance will suffer as well (signal loss or interference etc).
I hope this clears up some of the incorrect or confusing descriptions in this thread.