From my own experiences, the problems with this new skill system aren't inherently with the style and how it's presented, this sort of system can work well, and has in many other games that I have played. The main problem stems from how it's laid out, and what skills the player has to choose from at any given time. On many occasions, I have found myself leveling up and not being very interested in any of the options presented to me. This is a very bad thing, a player should ALWAYS be excited at each levelup, as it is a major milestone in any RPG. If nothing stands out or makes you excited for that next level, the system has failed.
I saw battle brothers brought up earlier in this thread, and I think it was an almost correct comparison. I do believe that battle brothers does this sort of system, but correctly because of a few key differences. The first, and most important to making things varied and interesting, is that battle brothers's skill tree completely opens up once you have invested 7 out of the 11 total skill points you get at max level. afterwards, you can pick and choose any perk from any tier without worry. The idea is that you are given less choices to not feel overwhelmed at first, something Star Sector is trying to do, but as you level up more, it opens up and allows complete freedom when you actually want it, which Star Sector doesn't do. It would be a very welcome change, in my opinion, if you could assign the final five skill points wherever you wished in SS. The secondary aspect that battle brothers does well is each new "Tier" of skills is carefully planned to have a viable option for any build, and what's more, you can instantly go back to any former tier and pick from there instead, which Still unlocks the next tier of skills.
So in essence, this system can be workable, but needs two things, a "Blossoming" skill tree that presents more and more options as you level, and careful planning in the skill unlock paths that assure every player will be able to pick something useful for their playstyle at every level. Getting rid of many of the false choices, like either high level officers or more, more productive colonies or more, and replacing them with actual choices could free up more space for this.