Again the point of the fed is to control interest rates, which is necessary when you are a foreign investor, or any investor. Who would invest in a country and buy the currency when they know that it is to the whims of any out side power and you can have high inflation or deflation happen at a moments notice.
Without foreign investment where do you think the US would be in the global economy, I can tell you it is not a good picture.
Yes with out the fed foreign banking institutions could use their own currency to manipulate the dollar directly.
Just because the fed does not operate in the way that it was supposed to does not mean it is a bad thing. I personally believe the policies of the fed should be looked at and reformed, not done away with so that the "markets" can take care of them.
With out the fed, if there was a large hit to the markets and something went wrong, and people would start to dump the dollar just for the fact that there was nothing to unsure that it would not be worthless the next day. That is the point of a central working banking system, to insure some sustainability to the countries currencies.
The fed also serves to insure that when I put money into the bank, and the bank goes under, my deposit is insures. Again another protection crucial to investment, and something that the markets will not protect. Remember the Great Depression...yeah that is what the fed protects against.
The fed, if it worked properly, insures that banking institutions have are regulated and they do not do stupid bets with other people's money. What we have seen in the past decade is not what happens when you have a central bank, but when you have central bank that does not work properly. It would have been a lot worse if we did not have a central bank when all of those banks went under.
Final Point:
There is no way in today's global enviroment you need a system to proctect your money against outside forces that wish to cheat the system. That is why we need a PROPERLY working central banking system. How does not market insure foriegn investments that the money is safe, protect average consumers from large banks betting with their money. It just can't.
Who do you think would control the "market". It is not some invisible hand, that idea is a illusions. Look a at the 1920's before the depression. It was controlled by and even smaller amount of people which completely desimated the world economy. At least this time around we had system to ensure that it was not as bad.
Supply and demand over simplifies what how money actually works in todays global diverse economy.