Well firs of all brink is not really made to be too realistic in my opinion. I mean does our military do flips and [censored] to kill each other? no they don't, besides REALISTIC IS BORING, its already been done by too many games and brink needs to be way different to truly succeed at becoming a new form of game play.
besides quickly pulling out a knife like in games such as modern warfare is not very realistic either
Parkour isn't in Brink "to kill each other" is a form of movement. Parkour was developed by the french military, and the troops took it home, which eventually evolved into the sport known as freerunning, which is more creative and less practical. Other militaries are also looking into applying parkour to urban environments, and the Ark would be perfect for it. So it isn't as unrealistic as you seem to think.
Everything in Brink is rooted in reality. From the artstyle dubbed "Hyper-Realism", to the weapons, to the technology, to the way parkour is being applied. The game may be exaggerated and not quite realistic at times, but there doesn't seem to be anything in the game that is totally fictional. So saying "realistic is boring" isn't an end-all argument for defending things you want to see in Brink. (or more accurately, the sequel, because there isn't anything new being put into the game at this point)
And finally, using a knife either way is fairly realistic. If a well trained soldier needs to remove someone silently, they will shoulder or holster their weapon, so they can use one hand to cover the victims mouth and use the knife in the other. On the other hand, in a dire situation, it wouldn't be hard to hold your rifle or pistol in your off-hand and quickly pull out your knife and go for a stab or slash.