It doesn't increase her skills as a ninja.
An eye used for ninja techniques doens't increase one's skill as a ninja when used. What a funny guy :lol
Being able to see more doesn't make you deadlier.
Actually it would, it just depends on who the opponent is. Neji could only see 50 m in Part 1, and because of that, Kidomaru took advantage of that weakness. Now have Hinata with 20 KM vision. It also allowed Bolt to find the Nue's weak spot, likewise for Neji with Kisame. Also allowed Hinata to see if her team was in a Genjutsu.
Let's takes some other examples: Byakugan would also allow to uncover Sasori's abilities, and Kakuzu's, and Deidara's, and Shino's. So yeah, it does provide an advantage in battle to the user.
Neji would be able to kill her in a fight,
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despite having the weaker eye.
Neji's eye isn't weaker, they're the same as I showed in the scan you keep denying.
In a fight, randomly awakening your Sharingan will do you better good than randomly awakening your Byakugan.
Never said otherwise, did I? Why do you feel so insecure you're bringing this up?
The Sharingan makes your previous skills ten times better rather than making you see through someones clothes.
Byakugan grants Chakra sight and precognition. Stop making stuff up.