Is it even possible to get "good" at this genre?
Yes it is, and it is also possible to get worse. I often play adventure games in parallel with other people, and I really measure the difference that m experience with "adventure game logic" makes. These games demand a certain mindset, a certain approach, that is less natural than acquired by encountering the same kind of puzzle many times over the years. What sort of thing to seek, or what sort of solution might work, becomes comparatively more obvious with time. Adventure games often re-skin the same clichés.
And on the other hand, I realised that I used to be better at some games than I am now. So, training is not acquired forever, thoughts habits may get lost with time and lack of training.
So, two advices maybe not given yet (not sure, only skimmed through the thread) :
1) Multiplayer. This point has been cleverly risen by Tim Schafer in his Full Throttle videos : Point and click adventure games were the first multiplayer games. Most of their fun derived from conversations and hints (and experience) sharing between concurrent players. It makes the games easier and more amusing. This was, paradoxically, killed by the internet, and its impersonnal walkthroughs.
2) Revisit locations. One annoying mechanism that plagues man aventure games is that you can visit a place, and some element may be missing or present depending on completel unrelated triggers (have you advanced the plot elewhere, talked to this character, picken up that item, visited a given area, encountered another puzzle, etc). It's expected when your adventures take place in a living breathing village as in Hero Quest/Quest for Glory, but it also happens with a tool present or absent from a corridor in Post Mortem. The consequence is that you can not rely on your memory or notes to know if, in front of a puzzle, there is something elsewhere that could help. Your memory or notes may be simply outdated, and you might have to go revisit each location.
Also, don't avoid deaths. These older games were less focused on senses of accomplishments than nowadays, they were playfully killing you and those were the jokes, it was part of the fun. Their deadends were often fun experiences (again, partly as experiences to share with other players).