@gentleshaid @enforcer48
I will try to address those questions in this common reply.
I think I need to add a little more perspective into it. Every time, there is an external pathogen or even internal damage the immune system needs to respond. What we have here is too strong an immune response or too weak an immune response or just right immune response.
Think of this way. When you get a wound on your skin, immune cells arrive there to clear up the mess and stop pathogens from entering. But this response is regulated by various brakes. After a while, these immune cells have to deactivate or die and stop messing around. If they don't you end up getting chronic wounds which never heals because the inflammation in the wound keeps damaging the tissue further. However, if there was no inflammation some microbes will digest and eat your tissue like it was a piece of bread.
Another example is the fever. Fever is caused by a signal generated by immune cells with effects the thermostat in your brain. This causes the temperature to increase and make the environment unsuitable for the pathogens to thrive. But after a certain point, too much temperature say above 104 degrees or having temperature for a long time can damage your own organs. So up to certain point fever might aid fighting germs but after that its self-damaging.
Same goes for cough. A reflex generated by the interaction between immune cells and neurons during a respiratory infection.
Then coming to bats - it is true that certain kind of immune responses to viruses is dampened in bats. In this paper, it is NLRP3 inflammasome response. Another example would be dampened response of STING pathway in bats to damaged DNA or DNA virus in the cells. But it's not completely true that bats don't do anything to keep the viral titers in check. For instance, some studies suggest that interferon response is constitutively active in certain bats esp for interferon A. Even in this paper you will notice that while NLRP3 expression was dampened in bat cells, other inflammatory genes under NFkB regulation were not as low.
Which brings us to the next question? Would anti-inflammatory drugs work? The thing again is you don't want to dampen your immune system blindly. It is required to do slow viral replication, clear up damaged tissue and even help in developing antibody and T cell-mediated immunity against the virus. IMO, what one may want to target are more specific pathways that causes much violent inflammation. For instance, this paper suggests testing NLRP3 inhibitors might be interesting. So it totally depends on the mechanism of action of anti-inflammatory in question.
Anyhow, thought would share some interesting links for further reading -