You missed hunting.
Conversely I think they could be homogenized into one single skill that has a lot more levels to it than the usual basic 7-tiers and thus more progression for those basic needs and use the "pick one" skill buffs to let you specialize a bit more into whatever you actually end up doing.
Instead of simply "unlocking them all", I motion that a LIMITED sharing of such gathering skills (and their bonus perks from its levels) be made possible via the settlements system. For example, having 1 of a profession would allow up to level 3 (of 7) shared with all other townsfolk when said professional has a level 7. Having two (or three) would unlock it up to 5 or 6. Level 7 Would be star-invested exclusive. This would (hopefully) increase freedom in players helping others out in other tasks, and would divest from the repetition of being "stuck" in a profession. This would also potentially open up hobbies (such as hunting) as a cultural pursuit.
I think that those skills are just fine being professions, but I am of the opinion that they should be unlocked by default. There is a way to do it using server commands that doesn't steal your first three stars, but it's kind of convoluted. Of every player started the game with the mining/logging/gathering skills unlocked by default, then it would be less of an issue. Alternatively, if they become a sort of Stat system like you are suggesting, they could make new professions to deal with the initial processing of those materials. Or fold them into existing professions, although I like the idea of essentially adding new low-tech professions that would be useful all the way to the late-game.
It will be nice. Quite similar idea in : https://feedback.play.eco/feature-suggestions/p/logger-miner…
Expanding in this idea with the current skills system (different from the one in my OP): 1. Mining, Logging, Gathering and Hunting could be specialties in the Survivalist Profession; 2. They should all cost one star instead of compounding with how many specialties you already have; 3. Current recipes of those professions should stay where they are now, the current skills renamed to Advanced Mining, Advanced Logging, Advanced Gathering, Advanced Hunting; This decouples tool efficiency and leveling up with manual work from crafting knowledge and gives the means for people to focus on activities they like such as chopping trees without the pressure of having to sell furniture, and the person who actually focus on crafting will hopefully get rock, ore, wood, crops sold.