I can tell that physicists don't understand black holes or spatial expansion because the current models can straightforwardly make perpetual motion machines.
First, get some unobtainium. A string with a tensile strength a few million times any known material should be sufficient. Wind the unobtainium around a spool, gear the spool onto a turbine, and lower one end into a black hole. From our perspective, the string has infinite space to fall into before it hits the event horizon, so the string can be fed into the hole indefinitely. The only difficulty is manufacturing the string for less than the turbine creates in power, but the force, and therefore the turbine output, is inversely proportional to the size of the black hole in question. The Schwarzschild radius decreases linearly with mass, but force increases as the square. A half mass size black hole pulls half as hard at a given distance, but is also half radius, which means it pulls twice as strongly at the event horizon.
Two bits of luck at this point. First, it is unobtainium, so I can make it as thin or as strong as necessary. Second, a suitably small black hole may evaporate quickly, but the string would, according to convention, replenish the black hole. (Even though we never see it reach the black hole.) Simply increase the force (and tensile strength) and lower the feeding speed until the turbine makes more energy than you're putting in.
There's also a reaction force to take into account, so these need to be built in pairs. Solid rings aren't orbitally stable, so I need slightly bigger turbines to power the stabilizing thrusters.
(For lulz, search up black hole perpetual motion and be amazed at how complicated they try to make it.)
The second method may need much stronger string, and costs much more to set up, but I don't have to worry about feeding the string slower than the black hole evaporates.
The velocity of other galaxies is not a normal kind of velocity. We see Doppler-shifted light because the space the wave is in expands while it is travelling through it; it just happens to work out to be exactly how much it would be redshifted by real velocity. Acceleration is absolute, because it usually requires transfers of energy and thus interactions and mass flows. Other galaxies are accelerating but not gaining kinetic energy, because otherwise we would be gaining kinetic energy. (Or I could say their velocity is changing without acceleration.) Nevertheless...
Tie the unobtainium around a couple rocks a few million light years away in opposite directions. They will accelerate away indefinitely, powering the spool turbines. Indeed, the output will increase the longer the machine is run. Though the friction losses alone will be immense, and the tension at the rock's end will grow faster, so it needs especially pure unobtainium.
Perpetual motion machines are singularities. If nothing else, potential energy has mass too, and so they should have infinite mass and subsequently destroy the universe.
You can try to argue that since these need unobtainium, they aren't naked singularities. In any realistic situation, limits of electromagnetic bonding and so on, the strings on the expansion machine will snap before they break even. Galaxies accelerate away from each other, and so won't ever turn this phantom kinetic energy into a collision. The black hole small enough to create more energy than it consumes in mass will evaporate so hot it burns the string to plasma.
However, the second law of thermodynamics is supposed to be true even in highly idealized mechanisms. A frictionless Carnot engine with zero switching costs between its infinite hot reservoir and infinite cold reservoir still cannot break even. All I need is a very strong kind of string. I could also use a ridiculously sized bit of piezoelectric.
To be precise, a Carnot engine feeding into absolute zero can be 100% efficient. However, my unobtainium spools can produce infinite energy for zero cost by turning an infinitely large turbine infinitely slowly with an infinitesimal string. This means if you back off from those infinities, you can get any amount of energy you might need.
Put another way, it is not feasible to make these machines profitable for humans, but if I did this with regular twine, while it break almost immediately, for that fraction of a second more energy would be coming out of the system than went into it, even though I wouldn't be able to capture most of it. If I can do it, nature is doing it, it is merely a question of when and where.
If something seems to be violating conservation of energy, it isn't, you've overlooked something. These models have overlooked something apparently infinite.
I find that physicists often, usually, forget that they don't understand black holes. Or space in general, it would seem - "shut up and compute" has laid low most of the field. To be charitable, do I assume they talk about it at physicist cocktail parties, just never in public? Not even during lectures?