While I am by no means an expert on track cycling, the one time I tried it at Hellyer (San Jose, CA) the coach there advised us newbie not to slow down by resisting the pedals with our legs. He cautioned that this action was bad for our knees and our leg muscles. He told us to instead just ride up the banking.
My position on brakes is that a rider on the street ought to have both a front amd rear brake for emergencies. Especially if you ride in the city or on hills. Just because you have a brake doesn't mean you have to use it. If you want to practice controlling your speed just with your cadence having a brake does not preclude that possibily.
However, if you need to stop right away and suddenly then the brakes will come into play. I feel for the safety of all, if you share the road with others then please mount brakes on your ride. Thank you