I think the OP's ideas are quite good, but TBH I am not sure they work well as fighting styles, they might be better suitable as feats.
There isn't any strict reason why they couldn't be fighting styles... it's just that the PHB fighting styles are conceived as bonuses/abilities related to a specific weapon configuration rather than weapon type, and by configuration I mean "how do you configure your hands to use weapons":
Archery: both hands using a ranged weapon
Dueling: one hand using a melee weapon (other hand up to you, as long as it's not another weapon)
Great Weapon Fighting: both hands using a melee weapon together
Protection: one hand using a shield (other hand up to you)
Two-Weapon Fighting: both hands using a melee weapon each
The main exception to this is the Defense fighting style which requires to wear armor. This also means it is actually compatible with all the other styles, otherwise the only other compatible combination is Dueling + Protection. IIRC this is relevant only for Champions who gain 2 fighting styles, and of course a Champion could pick two "incompatible" styles, it just means she won't normally benefit from both at the same time.
Archery is also slightly off, since it can be used with darts which require one hand only.
Besides the general melee vs ranged then, the fighting styles don't get more specific than that. Everything more specific on the weapon type or the kind of action you choose to do, it ended up as a feat instead. The main difference being, everyone can learn feats, but only Fighters, Paladins and Rangers can learn fighting styles. Even tho styles are more generic than feats, go figure!
If there's any miss from fighting styles IMO, it is one for thrown weapons, which normally require one hand, but attack at range. Unfortunately the Archery style doesn't work with them (see Sage Advice), either by design or mistake. It's possible that by the RAW the Dueling style might instead work, even if it might not be the RAI. I think that it would have been better for thrown weapons to have their own fighting style, to complete the picture.