> If you look into the way that hydrogen adsorbs into a platinum lattice, and how phonon resonance modes can induce tremendous crushing forces on anything between two platinum atoms, cold fusion actually looks quite plausible.
No, it is not. These things are well understood. The behaviour of hydrogen in crystals is studied a lot. In metals because of issues with hydrogen embrittlement and fusion stuff, in some oxides for the storage of hydrogen for energy applications, and in material in general because proton irradiation is a common tool when studying them. All of this to say that this is not something that was never investigated.
> It's not like perpetual motion--there's a clear possible mechanism for it which is surprisingly fully compatible with the laws of physics as we understand them.
The orders of magnitude just do not match. The pressures involved is typically 1 GPa (usually less in metals, more in ceramics). That is far from enough to bring nuclei sufficiently close for fusion. There is a reason why nobody claims this, and it is not because we don’t look at the behaviour of hydrogen (or other light nuclei like deuterium, tritium, helium, or lithium for that matter).
> The theory behind LK-99 is pretty solid. The linear structure of these apatite compounds create chains of conductive electron bands that in theory might have sufficient band gaps to enable superconductivity.
Again, it is not. Some preliminary electronic structure calculations showed interesting features, but these features were no indication of superconducting behaviour, and indeed LK-99 is not a superconductor. There were plenty of people who tried to reproduce the results and it clearly showed that the initial paper was wrong.
> If you could get atomic precision in the copper/lead alternating pattern that creates those stresses.
Our understanding of what causes superconductivity and the creation of Cooper pairs is not complete. Otherwise, we’d design materials with the right properties from the beginning, rather than testing a lot of stuff just to see what works.
> However I fear any research into room-temperature linear superconductors will now be as taboo as cold fusion.
Contrary to cold fusion, superconduction is actually a thing. Current high-temperature superconductors work at the temperature of liquid nitrogen; finding one that works 100K higher is not that much of a stretch. The gap is not 6 orders of magnitude like with cold fusion.
In fact, there is quite a lot of funding for research on high-temperature superconductors even this year so your fear is not really well founded.