Sort of. The center conductor is what is carrying the signal. The dielectric is irrelevant - you just need to know that it's there. It doesn't matter if it's plastic or foam or whatever, just understand that it's an insulator, and it's physically separating the shielding from the center conductor.
The center conductor is what you transfer the signal through. But if it were just the center conductor, without any shielding, you'd basically have one really long antenna. You would be losing signal through it, as well as gaining interference.
That's where the shielding comes in. It separates the outside environment from that of the center conductor. Therefore, the signals traveling through the center conductor are broadcast off into the dielectric, where they hit the shielding, but cannot escape. If the shielding was not present, they'd be broadcast into the surrounding environment. The shielding also acts as an interference barrier. Any signal outside the cable will hit the shielding and not pass through, therefore not impacting the signal.
The dielectric only has relevance in the fact that it's there. It doesn't matter what material it is made from, as long as its not conductive. So there is no possible way that the dielectric can break down. Unless, of course, you propose that somehow the dielectric suddenly gains a degree of conductivity, therefore shorting together the center conductor and shielding to some extent.
I'm not saying that RG59 is "just fine" for DPP. I have tried to make it clear that it is not ideal, and should not be used when avoidable.
However, the issues with RG59 and DPP are not this magical "burn-out". It has to do with signal attenuation of upper frequencies, which are used more in DPP than DP and Legacy. Typical RG59 attenuates 3000 mhz at about -17 db per 100 feet, while typical RG6 attenuates 3000 mhz at about -10 db per 100 feet. THAT ALONE is the issue with DPP and RG59. Over a long cable run...which can be the typical length from the distribution point to a room, the higher frequencies are attenuated too much and do not pass well.
There is no such thing as "burn out." Explain to me, in molecular terms, what happens when you try and pass higher freqencies through a cable that cannot pass them. Nothing. Absolutely nothing. They just don't pass. The cable doesn't heat up. Nor does some slow chemical reaction take place that degrades the conductivity of the copper or the insulation of the dielectric. Not happening.
Which is why your theory applies to RG6 too...if the cable is really being degraded, and RG6 is the same exact thing but with a thicker conductor, thicker dielectric, and more shielding, the same process will take place, just at a slower rate.