Your eyes are spaced horizontally. This makes it pretty easy to ignore narrow vertical elements: if one eye gets blocked there's a good chance the other eye can still see around it. The same thing doesn't go for horizontal elements. If one eye is blocked the other is likely to be blocked too: you'd need to move your head to see in that blind spot.

It'd make for a pretty neat research project, Make various sight obstructing hats with varying amounts and sizes of horizontal/vertical elements and see what its effects are on reaction speed, tracking a moving target, See if diagonal elements are better than horizontal ones etc etc.

In any case I can imagine a cage like that being annoying, but (to me at least) that doesn't really weigh up to the risk of injury.

Like wearing glasses, I imagine.

I used to play with a guy that had one of those half cages with visor top half, would be tempted to try that if I needed to replace mine, but not enough to get one before then.