So that it can spread the spores. Sorry I didn't go through the process step by step. Also we've been over this, the Cordyceps didn't inspire the game, the story or anything, but the infected.
No, because going through the whole process would have meant admitting you're wrong and the cordyseps don't 'just kill' their host they
control their host. This is the part that inspired Druckmann and what makes that BBC documentary so interesting. The cordyseps are parasites that 'infect' humans and 'control' them NOT mutate them. There are NO human mutants in the game just humans under the control of a parasite that infected them.
Runners are the first stage, stalkers are the second stage, clickers are the third stage and bloaters are the last stage. Each stage has a signature appearance in order to be able to identify the enemy and use a specific strategy to kill them. Each stage also represents the human losing more control until he no longer has any control at all. From runners (in which the human fights but can't stop the instinct to attack) to bloaters (in which the human has completely lost control and is nothing more than the instinct to kill).
Those humans that become nothing more than suppositories for the fungus and give off spores are DEAD humans because in order for the runners to exist the human has to be alive. Remember, these are not zombies. Cordyceps are not sentient and so regardless of host they will infect in the same way. Just like in the documentary, when the host is alive (in this case human) the Cordyseps will attempt to control the host, but once the host is dead then the fungus begins to function differently in order to create spores.
In order to make this a viable option for a video game, ND simply lengthened the time it takes and gave them slightly different motivations. They don't seek out height, they seek out uninfected humans.
This is why I think it's a better option to have other animals infected IF they want to add different enemy types. What comes after the bloater? Think about that for a moment because the process of deterioration is now set into the lore and it can't just suddenly take a left in order to add enemy types. Anything before the runners would simply be ill people, anything after the bloaters would simply be fatter, slower bloaters.
You wouldn't want the fungus suddenly growing tentacles or the humans to grow an extra head. It would feel stupid in TLOU universe and completely go against what Druckmann was going for. That concept art was rejected for a reason. I CAN see a couple of opportunities for a different human enemy though but it could really only be used once or twice. If two (or three) humans get infected together, it wouldn't be too much of a stretch to suggest the fungus could bind them together.