Should be edited to read "the way big old cities that have managed to survive seem to survive..."
That makes it a tautology, or at the very least, selection bias. You can't count the survival of surviving cities, while ignoring the non-survival of non-surviving cities as evidence that all cities survive. There are a lot of examples of big old cities that did not survive. Unless, of course, you only look at the last few hundred years, which is a very short-sighted view of history. Especially history as it might be applied to the deep future.
It's very uncomfortable to contemplate one's own individual mortality, and just as uncomfortable to contemplate the mortality of civilizations. But if history has taught us one thing it's that civilizations do NOT last forever. And if paleontology has taught us anything, it is that species do not last forever either. System become too complex to manage, and then they collapse. It's the natural order of things. It's just the way it goes. To think this generation is so smart it can avoid that natural cycle is like those folks who in 1929 told us the business cycle had been conquered and permanent prosperity had arrived.
In the final analysis it doesn't matter what I believe or what you believe. The inexorable laws of thermodynamics and the laws governing complex dynamical systems will grind on and on, oblivious to our opinions. The great machine will unwind, as all great machines do, and this civilization will end, as all great civilizations have in the past.