Hmm, well I guess I turned off game chat a long time ago. As you have observed, the only chat one receives is frequently extremely hostile.
Rather than stew about it, I turned it off. I had gotten used to tournament chess where no one would ever speak until the end of a game.
As to whether the reports you make have an effect, I do know that some players actually receive sportsmanship restrictions because they have come to the forums to complain about them.
I have received no less than 3 messages in the last week after games calling me among other things "moron", "stupid player" and like that. Now, this does not really bother me that much but is this really something that is part of the culture on chess.com? Because if it is I will not be paying for a membership here anymore.
I reported both users but can't see if anything has been done or will be done for that matter.