Two brake positions on fixed gear/single speed I recently bought a fixed gear/single speed with a flip flop hub. 
It has drop bars with two brake positions. One on the hood and one set of cross top brakes. 
I was considering removing the hood brakes, as having two sets looks a little silly (to me) on a fixed gear. 
I don’t know if the bike was originally a conversion or if it came this way. 

Would it be okay to remove the hood brakes and keep the cross bar brakes?

I do hope I worded everything appropriately! Thank you in advance for your advice.
You can use cross top levers without the main lever with some hacking. There is a thread about it here: https://www.bikeforums.net/singlespeed-fixed-gear/108969-how-install-inline-brake-lever-primary.html

You can also replace it with a 'normal' brake lever. If your bar is oversize (31.8 mm) it can be hard to find a brake lever that fits, but it's certainly doable.

Having two levers might not be such a bad idea though, since it means you have a brake lever within reach from all hand positions. But I'm planning on installing just a 'top' brake lever on my fixie, so I can certainly see your point. You can also put a TT bar end lever at the bottom of the drop and use the cross top lever as well. That will look 'cleaner' than the usual road hood thing.