Oooh bad example there.
For Neji fighting would have Byakugan switched on, and he could see through the genjutsu.
Remember when Kurenai taught teams 8 and Gai (minus Neji) about genjutsu that she mentioned there being "few highly advanced genjutsu" techniques that could fool the Byakuugan.
But I get the point.
Two points: Ironwolf had one right about the eye effects being useless if the mind behind the eyes isn't properly applied and the second being that not all shinobi have special eye techniques.
So what if it doesn't work against a specialized subset of shinobi with specialized visual techniques? They are a subset, not the majority. If you run into one, you change tactics and use a different tool. Sometimes you need a hammer, sometimes you need a screwdriver, but if all you have is a hammer everything looks like a nail. This is fundamentally the problem with specialized bloodlines. They limit themselves. It's a psychological blindspot that could easily become crippling.
Now lets' steal a thought from
The Way of the Appartment Manager, does all genjutsu have to have a visual effect? Instead of fooling the visual senses, fool the ears! Make the opponent think he's being targeted by kunai and shuriken from behind and force him to dodge into a position that is more favorable. Fool the sense of touch so that he thinks he drew his sword when he is actually weaponless. Fool his sense of self to make him think he's been poisoned because he tastes iron on his tongue and he's feeling lethargic.
In other words, yes, I think Hinata could easily incorporate genjutsu into her arsenal and do so in ways that would even fool her family.