I certainly have a different definition of what is evidence for a claim
No, you don't. You simply have no actual idea what the claim is.
I'm quite serious in believing that you don't understand thermodynamics. A thermodynamic limitation means that energy cannot be extracted because it violates a physical law. For example, we have a theoretical limit on how much energy can be extracted from a heat engine based on the temperatures of the heat sources and heat sinks. Irrespective of technology, we can't do better than those limits.
Of course, in practice we can't get anywhere near those limits. I think the best possible heat engines we can make are something like 5% efficient.
Similarly, we know the energy content of gasoline -- about 30 MJ/liter, which means we know (thermodynamically) there's no way to develop a gas-burning engine that can produce 50MJ of energy on a single liter of gas. Again, in "real life" we're nowhere near that limit.
Technology imposes a limit on what we can do today. Thermodynamics imposes a limit on what we can ever do. And technology is continuously improvi8ng.
...until you show or cite some calcs on how many quads/year with harnessing the rotation of the earth,
To a first approximation, the earth is a solid sphere with a 6000km radius, a mass of 6x10^24 kg, and an angular rotation of 0.00007. Rotational kinetic energy is defined as (1/2)(I)(w^2), which according to my envelope yields about 10^30 joules of energy, or about 10^12 quads. At 1000 quads/year, there is enough rotational energy there for "only" about a billion years.
Now, you're going to say "we can't tap that much energy out of the earth's rotation." And you're right -- FOR NOW. But that's not a thermodynamic limitation, but a technological one. We can build better and more efficient tidal generators, we can build generators we can deploy in new areas, and we can find other ways than ocean tides to tap into tidal energy (how about using Coriolis forces, for example?)
You can also use methane hydrate or dropping marbles into a black hole for the same level of evidence in the future...
Quite possibly. I don't know how much energy is trapped in methane hydrate world-wide, so I don't know how many quads of energy are theoretically available for extraction. I do know how many black holes are available within the orbit of the moon, and so I'm willing to dismiss dropping marbles into a black hole as a useful energy source for now. But the key word there is for now; a few breakthroughs in high energy physics from now, and we may be able to create and maintain artificial black holes and use them as energy sources.
You don't know what future technology will bring. And in the case of rotational energy, we know there's enough energy there to power human civilization for a hell of a long time. Thermodynamics says that it's possible, and all we need to do is figure out how.