Just like many people already have it.
And there it is. This is a not so thinly veiled post being highly judgemental about people on anti-depressants and the like.
As you've identified:
I'm sure that what me caring does to my mental state is far worse than however good is anything it does to anyone else.
So... if it's not helping anything, and arguably harming yourself, what is the point?
I promise you that it is possible to be aware of these horrible things going on, accepting that you cannot do anything about them, minimizing of the negative impact on your own emotions and mental state... and to be able to move on with your own life and enjoy what there is to enjoy around you. All at once.
That isn't a "lack of caring", it sure as hell isn't fucking ignorance. I honestly take quite a bit of offense at that.
It's basic acceptance of what you can and cannot change. The relatively recent idea that if you aren't emotionally distraught about world events then you don't care is one of the most toxic and damaging to mental health things in recent time.
Some people will call it stoicism, but it's not even going that far.
This whole idea of "I have to stay aware of all the suffering in the world, and I have to have strong feelings about all of it!" is just "thoughts and prayers" with a whole bunch of extra steps that people often use as justification to look down upon others who don't stay as up to date, or who don't get as emotionally invested.
So to answer your question, no. I wouldn't take pills that work as you describe.
Thankfully, that's not how anti-depressants and anti-anxiety medication fucking work! (Unless you're on far too high a dose or perhaps on anti-psychotics instead)