They don't detect the gravity of starships, either. And ships have gravity utterly disproportionate to their mass, pulling with a full gee on every deck...
Phaserproof barrels, or wall paintings, or carpets, should be a thing, yes. We see in ST6 how the phasing effect is selective, taking the kettle but not the contents - but it always has been selective, taking the Klingon but not the ground beneath his feet or the air around him. Apparently, a setting optimized for removing X does not readily remove Y if X and Y are suitably different. And if a phaser optimized for taking a humanoid doesn't harm a decorative painting or a plastic barrel, even though a phaser optimized for taking a plastic barrel is perfectly capable of doing so... Layered armor ought to be doable. At least if the enemy doesn't know the composition of the compositing in advance, and adjust the setting accordingly.
Which may be why Klingons and Cardassians wear utterly useless armor. It demonstrably can't stop knives or sharp rocks or fists, but it works against death rays until the enemy finds the proper setting. And the Feds just happen to be distressingly good at this analysis thing...
As for the Klingon mind-sifter, it never worked. They used it on Spock until satisfied with results, and those results were false. They did not care whether Spock lived or died there. They thus apparently would never use it further than that, and never discover anything useful with it - but, also, never manage to ruin a mind with it.
Timo Saloniemi