You're asking a bunch of fixed gear converts what they think. Of course they'll say you don't need it. That's the thing about the Internet, go to a certain board and it's an echo chamber towards a certain philosophy. Go ask the mtbr.com 29-incher forum about getting a 29-inch bike, they'll tell you it's the best ever. Ask about frame materials, and the retro SS/FG forum will say 'steel is real', and the roadie forum will say 'carbon is it'. Be conscious of that bias.

Personally, being a bit older, and cured of my youthful perception of immortality, I don't buy into the hype. Yes, fixed gears are harder, require far more dexterity and skill to pull off many urban evasion maneuvers, and requires retraining of your instincts. Yes, you need to pay more attention, and that means you have less available for other things, which means you're more likely to make mistakes. (It's called 'cognitive load', feel free to look it up.)

I'd say to ride with both brakes for several months until you've learned exactly what a fixed demands. That's what I'm doing, and based upon some of the panic stops I've had to make, I'm glad I did, and won't be removing my rear brake for now, if ever. Will you absolutely need the rear brake? Maybe, maybe not, but you won't know until later.

Just admit to yourself you want to get rid of it for one reason - style - and go from there.

PS - I don't expect you to listen. Everyone I ride with is 30 or older, and they all laugh at the idea of taking off any brake on an urban bike, fixed or not. The only person I know that goes without a rear brake on a city bike is one of the most talented and experienced riders I know, and even he won't take that bike out for more than a ten mile ride.