I disagree that a game goes downhill once a player is sent off. In fact the very fact that it totally changes the dynamics of the game means it can turn a really dull match into a lively one. Some of the greatest performances I have ever witnessed have been from teams down to 10 men who had been terrible before the red card but forced to play out of their very skins once a man light.
Besides, the issue is that the red card discourages professional fouls by reminding the players that a bad foul doesn't just punish them, it punishes the team. It's worked for over a century, I'm not really sure why it's becoming such a controversial point at present.
It's probably worth saying that I do also favour the reverting of refereeing standards to how it was about 20-30 years ago - i.e. it should be far harder to win a foul, fouls should only be given for occasions where there was a genuine risk of injury, not just for any situation where there's the slightest contest. Accordingly red cards IMHO should only be given for challenges where there is no attempt whatsoever to play the ball, or where serious injury could have occurred, so you'd still see a number less red cards if football were refereed how I picture it.
THIS 500% is where I am going with the above comment.