As fictional creations they are as fast or slow as the writer needs them to be in order to advance the plot. Original zombies were shambling and slow. They caught people through numbers and surprise. Or by pursuing the person until they made a wrong turn and got cornered. Shaun of the Dead plays on this older zombie concept.

Using your example of The Last of Us, there are several situations in which the main characters would absolutely have been killed were they not wearing full plot armor. But the zombie moved just a hair too slow, or got distracted, or went too fast and somehow overshoots. Or tackles them in just the perfect way to not be able to manage a bite. Never happens for the poor schmucks in the background though. Zombies run 'em down, pure focus, perfect aim. Tackle them mouth first, bitten in less than a second. Turned in 5 seconds. No hours long mournful transition allowing tearful goodbyes with loved ones.