i'm not sure it's entirely true that iq is immobile. i think same person taking iq test at age 4 vs 20 will perform differently, and not just because the default average of 100 shifts with new people taking it over time. i will posit that this same person at 20 will also perform differently depending on whether or not brain development was inhibited along the way (drugs, physical trauma to brain, etc). similarly, cognitive decline will definitely lower iq test performance (includes both permanent things like dementia, but also if you were to take an iq test while intoxicated or something). these are extreme examples, but it makes it clear that it's not fully "innate", there are at least some external things that will influence it, and others (general health, nutrition, etc) that might to a lesser degree that would be challenging to prove.
iq test has predictive value, but like other tests can be gamed. at present, there isn't much incentive to inflate iq though, so most people don't do it. it is used as a proxy/estimate for general intelligence, but this only works while the fact that "most people don't do it" remains true. it is possible to practice it, and if it were done at scale, it would be significantly less representative of general intelligence and more like grades on college exams...still predictive of *something*, but not general intelligence alone.
it does seem to be true that there are levels of general intelligence below which it becomes impractical to practice/study enough to succeed at difficult cognitive tasks, though. people above that threshold for any particular activity will generally just need more or less time/effort to master said activity depending on their baseline for it.
edit: doubt spamming hoi 4 will improve iq itself. if you really want to improve iq, practice iq tests. but you're probably better off doing something you enjoy, be that hoi or otherwise.