Given that you can change at least one of your weapon masteries each long rest, why do you even need to pick them? A character is only likely to want to use a weapon they lack mastery in if they happen to find a really cool magic weapon. And if it's not significantly better than what you are using, you are probably better off waiting until you've switched your mastery. The other scenarios are the equally rare situation where you have been unarmed and have to use what you find, or the even rarer one where there is a significant contextual benefit to using a specific available weapon other than the one you focus on.
So basically, the way it's set up, it doesn't define your character's style (since it can be easily changed), it just discourages you from doing cool things when they come up.
Seems like the system would be better (and save word count) if barbarian, fighter, paladin, ranger, rogues just got this feature instead:
Weapon Mastery
If you have proficiency in a weapon you can use its mastery property when you wield it.
(Edit: To clarify I'm not addressing masteries being tied to certain weapons--I'm accepting that as a given. I'm questioning the merit of characters having to choose which weapons they can use with mastery, rather than just getting to use every weapon with its appropriate mastery. I've updated the wording above to clarify.)
It's because they wanted fighters and barbarians to have more masteries than rangers, paladins, and rogues. This creates some distinction among those classes with weapon mastery where fighter > barbarian > paladin or ranger > rogue in the aspect of weapons that drastically changes with all weapon mastery being available. There would need to be additional changes to maintain that.
Sorry if this was already mentioned. I didn't have time to read the rest of the thread.